PolynomialsMath 9

Polynomials ActivityMath 9

Your Task #1

Your Task #2

Create 5 of your own expressions and record them on a piece of paper. Use at least 2 variables.

Your Task #3

Trade with somebody else and have them simplify the 5 expressions that you created. Record on your paper.

Your Task #4

What do you think a polynomial is?

Introduction to PolynomialsMath 9

Review

● A polynomial is one term or the sum or difference of terms whose variables have whole-number exponents.

● Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it really means "many terms".

Polynomials

For an expression to be a polynomial term, it must contain no square roots of variables,

no fractional or negative powers on the variables, and no variables in the denominators

of any fractions. Here are some examples:

Degree

The term with the greatest exponent determines the degree of the polynomial.

Examples

Polynomial Constant Coefficient (s) Variable (s) Degree

x + 4 4 1 x 1

-2x - 8

3x2 + 3y

2y2 + 4y + 6

22

Simplifying Polynomials

Example

Miss McCormick has a basket of fruit in each hand. One basket contains 2 apples, 6 oranges, and 8 mangoes. The other basket contains 3 apples, 2 oranges, and 2 mangoes. Model and add the fruit using polynomials.

Examples

Example

Assignment

Page 214

#’s 4, 5, 6, 9, 10, 20

AND

Page 222

#’s 6, 7, 12, 13, 22

Adding PolynomialsMath 9

Review

To add polynomials, we combine the like terms. There are two ways to do this.

Examples

Examples

Example

Example

Assignment

Page 228

#’s 8, 12, 15, 17

Subtracting PolynomialsMath 9

Review

When subtracting integers, we always combine the middle signs, then add or subtract where appropriate.

Examples

Examples with Polynomials

Next step:

Recall

Subtracting Polynomials

(a + 1) – (-3a + 2) Distribute to both terms & remove brackets

= (a + 1) + 3a – 2 Change signs

= a + 1 + 3a – 2 Re-arrange like terms

= a +3a +1 – 2 Combine like terms

= 4a – 1

Examples

Assignment

Page 234

#’s 5, 8, 10, 12, 13, 15 (a, c, e)

Multiplying and Dividing Polynomials by a ConstantMath 9

Review

● Remember that when numbers and letters are side by side it indicates multiplication

● 4nm means 4 x n x m● In a multiplication, switching the order of numbers and

variables does not change the product ● 4nm is the same as nm4 or n4m or m4n

Examples

Examples

Determine the product.

Dividing

Examples

Determine the quotient.

Examples

Assignment

Page 246

#’s 7 (a), 8 (a), 12, 15, 16, 19 (a), 22 (a, c, e)

Multiplying and Dividing Polynomials by a MonomialMath 9

Review

When multiplying polynomials, each term from one polynomial must be multiplied by each term of the other polynomial.

When multiplying monomials, use the product rule for exponents:

xm × xn = xm + n

Examples

Review

When dividing polynomials, each term in the numerator must be divided by each term in the denominator.

When dividing monomials, use the quotient rule for exponents:

xm ÷ xn = xm - n

Examples

Examples

Assignment

Page 255

#’s 9 (a), 10 (a), 12, 14, 16, 22

Evaluating PolynomialsMath 9

Evaluating Polynomials Example

Evaluate the polynomial if x = 2.

6x2 + 3x + 6

Evaluating Polynomials Example

Evaluate the polynomial if x = 2 and y = 4.

20 - 2xy

Polynomial Review StationsMath 9

Polynomial StationsStation One - Polynomial Jeopardy (NEED A COMPUTER)

Station Two - Polynomial Identification (NEED TWO COMPUTERS)

Station Three - Evaluate the Polynomial (NEED TWO COMPUTERS)

Station Four - Polynomials Battleship (NEED TWO COMPUTERS)

Station Five - A Dicey Polynomial Situation (NEED TWO DIE, POLYNOMIAL CARDS, AND RECORDING SHEETS)

Station Six - Polynomial Bullseye (NEED A BULLSEYE SHEET PER STUDENT)

Station Seven - Polynomial Stick Sort (NEED TWO SETS OF POLYNOMIAL POPSICLE STICKS)

Station Eight - WhoDunnit Combining Like Terms Mystery (NEED ONE BOOKLET PER STUDENT)

Station Nine - Adding and Subtracting Polynomials Race (NEED ONE SHEET PER STUDENT)

Review

Page 259-261

#’s 2, 3, 5, 12, 15, 19, 22, 23, 26, 28

Practice Test Page 262