PolynomialsPolynomials

Adding and Adding and Subtracting Subtracting PolynomialsPolynomials

Adding PolynomialsAdding Polynomials

• To add polynomials, combine like terms.

+

+

+

=

=

2

2

2

Does not =

ExampleExample

• Add (-7z2 + 9z – 3) + (8z2 – 6z + 9)

(-7z2 + 9z – 3) + (8z2 – 6z + 9)

= -7z2 + 8z2 + 9z – 6z – 3 + 9

= 1z2 + 3z + 6

= z2 + 3z + 6

Rearrange the terms so that the like terms are grouped together.

Add like terms.

1z2 = z2

Finding the Opposite Finding the Opposite of a Polynomialof a Polynomial

• When a negative sign precedes parentheses, we find the opposite of the expression by changing the sign of each term inside the parentheses.

ExampleExample

• Simplify. –(–5a + 3b – 7c)

–(–5a + 3b – 7c) =

– in front of parentheses

We change the sign of each term

5a 3b 7c– +

Subtracting Two Subtracting Two PolynomialsPolynomials

• To subtract two polynomials, change the sign of each term in the second polynomial and then add.

ExampleExample

• Perform the operations indicated. • (3a2 + 4a – 7) – (7a2 – 2a – 5)

= 3a2 + 4a – 7 + (– 7a2) + 2a + 5

A – sign in front of parentheses indicates we are subtracting.

We change the sign of terms that were inside parentheses, then add.

= 3a2 + 4a – 7 + (– 7a2) + 2a + 5Simplify by combining like terms.

= -4a2 + 6a – 2

Multiplying Multiplying PolynomialsPolynomials

ExampleExample

• Multiply. -2y(5y2 + 3y – 8)

-2y(5y2 + 3y – 8) = -2y(5y2) – 2y(3y) – 2y(– 8) Multiply each term by -2y

= -10y3 – 6y2 + 16y

ExampleExample

• Multiply. (3x + 1)(x - 2)

(3x + 1)(x - 2)

First

Outer

Inner

Last

First

F

Outer

O

Inner

I

Last

L

3x2 - 6x x - 2

(3x + 1)(x – 2) = 3x2 – 5x - 2 Combine like terms.

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