9.7 SYNTHETIC DIVISION

DIVIDE THE POLYNOMIALS USING LONG DIVISION

a.

b.

x2 +10x+ 21( ) ÷ x+ 3( )

6x3 −x2 −5x+ 4( ) ÷ 3x−2( )

To simplify this process, we can use a process called division.

Synthetic division works when dividing a polynomial by .

To get started, make sure the polynomial is arranged in order of powers. Make sure to use a for any missing term. Write for the divisor, and the of the polynomial for the dividend.

x−c

synthetic

descendingzero

coefficientsc

DIVIDE USING SYNTHETIC DIVISION

1. x3 + 4x2 −5x+ 5( ) ÷ x−3( )

DIVIDE USING SYNTHETIC DIVISION

2. 5x3 + 6x+ 8( ) ÷ x+ 2( )

DIVIDE USING SYNTHETIC DIVISION

3. x3 −7x−6( ) ÷ x+ 2( )

DIVIDE USING SYNTHETIC DIVISION

4. 7−11x−3x2 + 2x3( ) ÷ x−1( )

The Remainder Theorem:

If the polynomial is divided by , then the remainder is .

f x( ) x−cf c( )

USE SYNTHETIC DIVISION TO EVALUATE THE FUNCTION. CHECK YOUR ANSWER USING SUBSTITUTION.

5. 6.

T x( ) =3x5 −4x3 −10x2 −7x−10

T −1( ) T 2( )

If the remainder is , that means that , and therefore c is a

of the function.

zero

rootf c( ) =0

Use synthetic division to evaluate the function

7. T 2i( )

T x( ) =3x5 −4x3 −10x2 −7x−10