Synthetic Division and Zeros

Synthetic division• Only applies when the divisor is x-c and when every

descending power of x has a place in the dividend• Eliminate all variables and use tidy columns

Synthetic division• Use synthetic division for

4 2(4 2 1) ( 2)x x x x

Answer• Line up the columns and fill in zeros for missing powers

4 2

3 2

(4 2 1) ( 2)

4 0 2 1 12

-8 16 -28 58

4 -8 14 -29 59

59Result: 4x 8 14 29

2

x x x x

x xx

Synthetic division• Use synthetic division for

3 2( 2 4 1) ( 1)x x x x

Answer• Line up the columns and fill in zeros for missing powers

3 2

2

( 2 4 1) ( 1)

1 2 4 11

1 -1 -5

1 -1 -5 4

4Result: 5

1

x x x x

x xx