POLYNOMIAL NOTES Day #2
Transcript of POLYNOMIAL NOTES Day #2
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Combine Like Terms1) 3x – 6 + 2x – 8
2) 3x – 7 + 12x + 10
3) 10xy + 5y – 6xy – 14y
5x – 14
15x + 3
4xy – 9y
Warm up
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PolynomialPolynomialOperations Operations
& Rules& Rules
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VOCABULARYVOCABULARY
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DegreeThe exponent for a variable
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Degree of the Polynomial
Highest (largest) exponent of the polynomial
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Standard Form
Terms are placed in descending order by the DEGREE
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Leading Coefficient
Once in standard form, it’s the 1st NUMBER in front of the variable (line leader)
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# of Terms
Name by # of Terms
1 Monomial
2 Binomial
3 Trinomial
4+ Polynomial
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Degree(largest
exponent)
Name by degree
0 Constant
1 Linear
2 Quadratic
3 Cubic
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2 9y Special Names:
LinearBinomi
al
Degree Name:
# of Terms Name:
Leading Coefficient: -2
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334xSpecial Names:
CubicMonomi
al
Degree Name:
# of Terms Name:
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24 6x xSpecial Names:
Quadratic Binomi
al
Degree Name:
# of Terms Name:
Leading Coefficient: 4
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3 27 2y y y Special Names:
CubicTrinomial
Degree Name:
# of Terms Name:
Leading Coefficient: 1
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Adding Polynomial
s
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2 22 4 3 5 1x x x x
1.
3x2 + x + 2
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26 2 8x x 2.
x2 + 2x – 2
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Subtracting
Polynomials
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When SUBTRACTING polynomials
Drop the 1st parenthesis then distribute the NEGATIVE to the 2nd parenthesis.
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2 23 10 8a a a a
3a2 + 10a – 8a2 + a
– 5a2 + 11a
3.
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2 23 2 4 2 1x x x x
3x2 + 2x – 4 – 2x2 – x + 1
x2 + x – 3
4.
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PRACTICE
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ANSWERS
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Multiplying
Polynomials
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The Distributive PropertyLook at the following expression:
3(x + 7) This expression is the sum of x and 7 multiplied by 3.
To simplify this expression we can distribute the multiplication by 3 to each number in the sum.
(3 • x) + (3 • 7)
3x + 21
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Multiply: (x + 2)(x – 5)
Though the format does not change, we must still distribute each term of one polynomial to each term of the other polynomial.
Each term in (x+2) is distributed to each term in (x – 5).
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(x + 2)(x – 5)
This pattern for multiplying polynomials is called FOIL.
Multiply the First terms.
Multiply the Outside terms.
Multiply the Inside terms.
Multiply the Last terms.
F
O
I
L After you multiply, collect like terms.
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Example: (x – 6)(2x + 1)
x(2x) + x(1) – (6)2x – 6(1)
2x2 + x – 12x – 6
2x2 – 11x – 6
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-2x(x2 – 4x + 2)
3 22 8 4x x x
5.
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(x + 3) (x – 3)
6.
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(3x – 1)(2x – 4)
26 14 4 x x
7.
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8. Find the area of the rectangle.
228 96 80 x x
7 10x
4 8x
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9. Find the volume.
3 29 18 x x x
3x
6x
x
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PRACTICE
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ANSWERS
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MORE PRACTICE…YAY!
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ANSWERS #2