Intermediate Algebra (11th edition)

Additive inverse

Signs changed

Remainder

3 x^2 + 9 x+ 25 +

80

x- 3

3 9 25 80

92775

3  30 - 25

724 APPENDIX B Synthetic Division

The quotient is read

from the bottom row.

The first three numbers in the bottom row are the coefficients of the quotient poly-

nomial with degree 1 less than the degree of the dividend. The last number gives the

remainder.

This shortcut procedure is called synthetic division.It is used only when divid-

ing a polynomial by a binomial of the form

Using Synthetic Division

Use synthetic division to divide by

We change into the form by writing it as

where

Now write the coefficients of placing to the left.

leads to Coefficients

Remainder

The result is read from the bottom row.

NOW TRY

Using Synthetic Division with a Missing Term

Use synthetic division to find

- 4 - 7 - 8 - 14 - 28 - 6

- 8 - 14 - 16 - 28 - 56

2 -41 6 2 0 50

1 - 4 x^5 + x^4 + 6 x^3 + 2 x^2 + 502 , 1 x- 22.

EXAMPLE 2

5 x^2 + 16 x+ 15

x+ 2

= 5 x+ 6 +

3

x+ 2

563

- 10 - 12

- 2  51615

56

- 10 - 12

- 2  51615

5

- 10

- 2  51615

x+ 2 - 2. - 2  51615

5 x^2 + 16 x+15, - 2

x+ 2 =x- 1 - 22 , k=-2.

x+ 2 x-k

5 x^2 + 16 x+ 15 x+2.

EXAMPLE 1

xk.

Use the steps given above,

first inserting a 0 for the

missing x-term.

NOW TRY
EXERCISE 1
Use synthetic division
to divide.

4 x^3 + 18 x^2 + 19 x+ 7

x+ 3

NOW TRY ANSWERS

1. 
   

2. 
   
   
   
   • 3 x^3 +x^2 - 2 x- 8 +x--^14
   
   
   
   

4 x^2 + 6 x+ 1 +x+^43

NOW TRY
EXERCISE 2
Use synthetic division
to divide.

• 3 x^4 + 13 x^3 - 6 x^2 + 31
  x- 4

Read the result from the bottom row.

NOW TRY

- 4 x^5 + x^4 + 6 x^3 + 2 x^2 + 50

x- 2

= - 4 x^4 - 7 x^3 - 8 x^2 - 14 x- 28 +

- 6

x- 2

Bring down the 5, and

multiply:

Add 16 and getting 6,

and multiply 6 and to

get

Add 15 and -12,getting 3.

• 
  
  
  
  12. 
      
  
  
  
  
  
  
  • 2
  
  
  
  


• 10,


• 2 # 5 =-10.