CLASSIFYING POLYNOMIALS
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Transcript of CLASSIFYING POLYNOMIALS
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CLASSIFYING CLASSIFYING POLYNOMIALSPOLYNOMIALS
by:
GLORIA KENT
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Today’s Objectives:
Classify a polynomial by it’s degree. Classify a polynomial by it’s number of
terms “Name” a polynomial by it’s “first and
last names” determined by it’s degree and number of terms.
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Degree of a PolynomialDegree of a Polynomial
The degree of a polynomial is calculated by finding the largest exponent in the polynomial.
(Learned in previous lesson on Writing Polynomials in Standard Form)
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn
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Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn “nth” degree
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9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn “nth” degree “nth” degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
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Let’s practice classifying polynomials by “degree”.
POLYNOMIAL1. 3z4 + 5z3 – 72. 15a + 253. 1854. 2c10 – 7c6 + 4c3 - 95. 2f3 – 7f2 + 16. 15y2
7. 9g4 – 3g + 58. 10r5 –7r9. 16n7 + 6n4 – 3n2
DEGREE NAME1. Quartic2. Linear3. Constant4. Tenth degree5. Cubic6. Quadratic7. Quartic8. Quintic9. Seventh degree
The degree name becomes the “first name” of the polynomial.
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
25x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term25x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial25x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial25x
3x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms
25x
3x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
25x
3x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
25x
3x 37 2 4x x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms
25x
3x 37 2 4x x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
25x
3x 37 2 4x x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
25x
3x 37 2 4x x
4 3 22 2 5x x x x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
Four (or more) terms
25x
3x 37 2 4x x
4 3 22 2 5x x x x
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Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
Four (or more) terms
Polynomial with 4 (or more) terms
25x
3x 37 2 4x x
4 3 22 2 5x x x x
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Classifying (or Naming) a Polynomial by Number of Terms
25
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8 4 (or more) terms
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8 4 (or more) terms
Polynomial with 4 terms
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8 4 (or more) terms
Polynomial with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8 4 (or more) terms
Polynomial with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7 6 terms
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Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term Monomial
25h3 + 7 2 terms Binomial
3t7 – 4t6 + 12 3 terms Trinomial
4b10 + 2b8 – 7b6 - 8 4 (or more) terms
Polynomial with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7 6 terms Polynomial with 6 terms
The term name becomes the “last name” of a polynomial.
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Let’s practice classifying a polynomial by “number of terms”.
Polynomial
1. 15x
2. 2e8 – 3e7 + 3e – 7
3. 6c + 5
4. 3y7 – 4y5 + 8y3
5. 64
6. 2p8 – 4p6 + 9p4 + 3p – 1
7. 25h3 – 15h2 + 18
8. 55c19 + 35
Classify by # of Terms:
1. Monomial2. Polynomial with 4 terms
3. Binomial
4. Trinomial
5. Monomial6. Polynomial with 5 terms
7. Trinomial
8. Binomial
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2
2x
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
2x
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
2x
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7
5b2
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Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
5b2
![Page 65: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/65.jpg)
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
5b2
![Page 66: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/66.jpg)
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2
![Page 67: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/67.jpg)
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
![Page 68: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/68.jpg)
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
1 term (monomial)
![Page 69: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/69.jpg)
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
1 term (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
1 term (monomial)
Quadratic Monomial
![Page 70: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/70.jpg)
. . .more polynomials. . .5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 71: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/71.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 72: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/72.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 73: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/73.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 74: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/74.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 75: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/75.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 76: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/76.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 77: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/77.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 78: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/78.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 79: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/79.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7
7f3 – 2f2 + f
9k4
![Page 80: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/80.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
7f3 – 2f2 + f
9k4
![Page 81: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/81.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
7f3 – 2f2 + f
9k4
![Page 82: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/82.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f
9k4
![Page 83: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/83.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
9k4
![Page 84: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/84.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
9k4
![Page 85: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/85.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4
![Page 86: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/86.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
![Page 87: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/87.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
1 term (monomial)
![Page 88: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/88.jpg)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
1 term (monomial)
Quartic Monomial
![Page 89: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/89.jpg)
. . .more polynomials. . .9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 90: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/90.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 91: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/91.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 92: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/92.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 93: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/93.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 94: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/94.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 95: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/95.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 96: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/96.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 97: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/97.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 98: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/98.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 99: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/99.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 100: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/100.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 101: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/101.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
![Page 102: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/102.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
j7 - 2j5 + 7j3 - 8
![Page 103: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/103.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (trinomial)
j7 - 2j5 + 7j3 - 8
![Page 104: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/104.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (trinomial)
Quintic Trinomial
j7 - 2j5 + 7j3 - 8
![Page 105: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/105.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (trinomial)
Quintic Trinomial
j7 - 2j5 + 7j3 - 8 7th degree (7th degree)
![Page 106: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/106.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (trinomial)
Quintic Trinomial
j7 - 2j5 + 7j3 - 8 7th degree (7th degree)
4 terms (polynomial
with 4 terms)
![Page 107: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/107.jpg)
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)Quartic Binomial
9k4 + 3k2 + 2 4th degree (quartic)
3 terms (trinomial)
Quartic Trinomial
v5 5th degree (quintic)
1 term (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (trinomial)
Quintic Trinomial
j7 - 2j5 + 7j3 - 8 7th degree (7th degree)
4 terms (polynomial
with 4 terms)
7th degree polynomial with 4 terms
![Page 108: CLASSIFYING POLYNOMIALS](https://reader036.fdocuments.in/reader036/viewer/2022062301/568151d6550346895dc0112d/html5/thumbnails/108.jpg)
Can you name them now? Give it a try. . . copy and classify (2 columns):
POLYNOMIAL1. 5x2 – 2x + 32. 2z + 53. 7a3 + 4a – 124. -155. 27x8 + 3x5 – 7x + 4
6. 9x4 – 37. 10x – 1858. 18x5
CLASSIFICATION / NAME
1. Quadratic Trinomial
2. Linear Binomial
3. Cubic Trinomial
4. Constant Monomial5. 8th Degree Polynomial with
4 terms.
6. Quartic Binomial
7. Linear Binomial
8. Quintic Monomial
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. . .more practice. . .9. 19z25
10. 6n7 + 3n5 – 4n
11. 189
12. 15g5 + 3g4 – 3g – 7
13. 3x9 + 12
14. 6z3 – 2z2 + 4z + 7
15. 9c
16. 15b2 – b + 51
9. 25th degree Monomial
10. 7th degree Trinomial
11. Constant Monomial
12. Quintic polynomial with 4 terms
13. 9th degree Binomial
14. Cubic polynomial with 4 terms.
15. Linear Monomial
16.Quadratic Trinomial
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Create-A-Polynomial Activity:• You will need one sheet of paper, a pencil, and your
notes on Classifying Polynomials.• You will be given the names of some polynomials.
YOU must create a correct matching example, but REMEMBER:– Answers must be in standard form.– Each problem can only use one variable throughout the
problem (see examples in notes from powerpoint).– All variable powers in each example must have DIFFERENT
exponents (again, see examples in notes from powerpoint).– There can only be one constant in each problem.
• You will need two columns on your paper. – Left column title: Polynomial Name– Right column title: Polynomial in Standard Form.
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Create - A – Polynomial Activity: Copy each polynomial name. Create your own polynomial to match ( 2 columns). Partner/Independent work (pairs).
1. 6th degree polynomial with 4 terms.
2. Linear Monomial
3. Quadratic Trinomial
4. Constant Monomial
5. Cubic Binomial
6. Quartic Monomial
7. Quintic polynomial with 5 terms.
8. Linear Binomial
9. Cubic Trinomial
10. Quadratic Binomial
11. Quintic Trinomial
12. Constant Monomial
13. Cubic Monomial
14. 10th degree polynomial with 6 terms
15. 8th degree Binomial
16. 20th degree Trinomial