3.1 Adding, Subtracting and Multiplying Polynomials

11/26/2012

Example 1 Add Polynomials Vertically

a. Add and2x 3 x 9+4x 2+ – x 3 5x 16x 2– + –

3x 3 4x 82x 2– + +

SOLUTION

2x 3 x 9+4x 2+ –

x 3 5x 16x 2– + –+

a.

Example 1 Add Polynomials Horizontally

b. Add and5x 2 2x+ 4x 2 37x– +

b. 5x 2 2x+ 4x 2 37x– +( ) + ( )

5x 2 4x 2+ 2x 37x– +( ) + ( )=

9x 2 35x– +=

Group like terms.

Combine like terms.

Example 2 Subtract Polynomials

SOLUTION

Align like terms, then add the opposite of the subtracted polynomial.

6x 3 7x 12x 2– + –

3x 3 9x4x 2+ +( )–

6x 3 7x 12x 2– + –

3x 3 9x4x 2+ – – –

3x 3 2x5x 2– – 12–

(3

Example 3 Use the Distributive Property

Simplify the expression.

2x 2 5x– + x 2 73x+ –( ) ( )+4 2

146x+8x 2 204x–= – Use distributive property.

+ + 2x 2

6x+8x 2 4x2x 2 –= Group like terms.

( ) + ( )+ + ( )20 – 14

10x 2= Combine like terms.

2x+ 6+

a.

Example 3 Use the Distributive Property

= Use distributive property.

x 4 x 3 ++ x 2 x+ x 3 x 2 x+– – 1–

= Group like terms.

x 4 x 3+ + 1–( )x 3– x 2+ ( )x 2– x( x ) –

= Combine like terms.

x 4 2x+ 1–

Review: Product of Powers:

Ex. x2 • x5

= x • x • x • x • x • x • x = x7

= x2+5

In general: am•an = am+n

Example 4 Multiply Polynomials Vertically

Find the product .( )x 2 4x 7–+ ( )2x –

SOLUTION

Line up like terms vertically. Then multiply as shown below.

x 2 4x 7–+

2x –×

2x 2 8x + 14–– Multiply by 2.x 2 4x 7–+ –

x 3 7x+ –4x 2 Multiply by x.x 2 4x 7–+

x 3 15x+ –2x 2 + 14 Combine like terms.

Example 5 Multiply Polynomials Horizontally

Find the product.

( )4+3x ( )5x 2 x 6–+a.

4+3x( )5x 2 x 6–+ ( )5x 2 x 6–+= Use distributive property.

SOLUTION

( )4+3x ( )5x 2 x 6–+a.

+15x 3 18x–+ 20x 2 4x 24–+= 3x 2 Use distributive property.

15x 3 + 24–+= 20x 23x 2( )+ 18x 4x– +( ) Group like terms.

15x 3 14x–+= 23x 2 24– Combine like terms.

Homework:

Worksheet 3.1 do ALL