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Polynomials

Defining Polynomials

Adding Like Terms

Slide 2

Monomials - a number, a variable, or a product of a number and one or more variables. 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials.

Polynomials – one or more monomials added or subtracted

4x + 6x2, 20xy - 4, and 3a2 - 5a + 4 are all polynomials.

Vocabulary

Slide 3

Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers.

Which terms are like? 3a2b, 4ab2, 3ab, -5ab2

4ab2 and -5ab2 are like.

Even though the others have the same variables, the exponents are not the same.

3a2b = 3aab, which is different from 4ab2 = 4abb.

Slide 4

Like Terms

Constants are like terms.

Which terms are like? 2x, -3, 5b, 0

-3 and 0 are like.

Which terms are like? 3x, 2x2, 4, x

3x and x are like.

Which terms are like? 2wx, w, 3x, 4xw

2wx and 4xw are like.

Slide 5

Add: (x2 + 3x + 1) + (4x2 +5)

Step 1: Underline like terms:

Step 2: Add the coefficients of like terms, do not change the powers of the variables:

(x2 + 3x + 1) + (4x2 +5)

Notice: ‘3x’ doesn’t have a like term.

(x2 + 4x2) + 3x + (1 + 5)

5x2 + 3x + 6

Slide 6

Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms!

Adding Polynomials

(x2 + 3x + 1) + (4x2 +5)

5x2 + 3x + 6

(x2 + 3x + 1)

+ (4x2 +5)

Stack and add these polynomials: (2a2+3ab+4b2) + (7a2+ab+-2b2)

(2a2+3ab+4b2) + (7a2+ab+-2b2)

(2a2 + 3ab + 4b2)

+ (7a2 + ab + -2b2)

9a2 + 4ab + 2b2

Slide 7

Adding Polynomials

Add the following polynomials; you may stack them if you prefer:

Slide 8

Subtract: (3x2 + 2x + 7) - (x2 + x + 4)

Step 1: Change subtraction to addition (Keep-Change-Change.).

Step 2: Underline OR line up the like terms and add.

(3x2 + 2x + 7) + (- x2 + - x + - 4)

(3x2 + 2x + 7)

+ (- x2 + - x + - 4)

2x2 + x + 3

Slide 9

Subtracting Polynomials

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