1 . 8 x 3 3 2 4x x

2 . ( )1 2 2 3 22x x x

Aim: How do we divide polynomials?

8 x 3 3 2 4x x

Divide each term of the polynomial by the monomial.

8

2 4

3

2 4

3x

x

x

x

Factor each expression.

8

3 8

3

3 8

2

x x

x

x

x

Divide out the common factors in each expression.

8

3 8

3

3 8

2

x x

x

x

x

Write in simplified form.

x 2

3

1

8

( )1 2 2 3 22x x x

Divide each term of the polynomial by the monomial.

Factor each expression.

Divide out the common factors in each expression.

Write in simplified form.

1 2

2

2

2

3

2

2x

x

x

x x

2 6

2

2

2

3

2

x x

x

x

x x

2 6

2

2

2

3

2

x x

x

x

x x

6 13

2x

x

Dividing a Polynomial by a Polynomial

The objective is to be able to divide a polynomial by a polynomial by using long division.

Dividend – the number which is being divided.

Divisor – The number that is being divided into the dividend.

Quotient – The result obtained when numbers or expressions are divided.

Remainder – The part that is left over when the divisor no longer goes into the dividend a whole number of times.

Polynomial Long Division

D iv id e b y x x x2 3 1 2 .

Step 1: Write it as you would a regular long division problem.

x x x 2 3 12

The x+2 is the divisor and the x2+3x-1 is the dividend.

Step 2

x x x 2 3 12

x

x x

x

2

1

1x x x 2 32

2

Divide x2 by x to get x. Place this on top.

Multiply x+2 by x to get x2 +2x.Subtract the x2+2x from the x2+3x-1.

Step 3

Divide the x by x to get 1.

Multiply x+2 by 1 to get x+2.

Subtract x+2 from the x-1.

x

2

3

1

3

2

2

2

x x xx

x x

x

2 1

1

Step 4

Write your final answer.

x x x

xx

2 3 1 2

13

2

d iv id ed b y is

The x+1 is the quotient.

T h e -3

x + 2 is th e rem ain d er.

1 . x - 2x x2 1 5

2 . 1 2 5 1 0 4 12x x x

A

A

x x2 1 5 x - 2

x x xx

x x

x

x

2 153

2

3 15

3 6

9

2

2

X2 divided by x is x. Multiply x-2 by x.

Subtract

3x divided by x is 3. Multiply x-2 by 3.

Subtract xx

39

2You Try It

1 2 5 1 0 4 12x x x

3 2x104 1 12 52x x x

3212x x

8 10x

8 2 x

8

T he so lu tion is 3 28

4 1x

x

.

12x2 divided by 4x is 3x.

Multiply 4x-1 by 3x.

Subtract

8x divided by 4x is 2. Multiply 4x-1 by 2.

Subtract

You Try It

Divide:

1. 3252 xxx

2.

42155 223 xxxxx