Dividing Polynomials

The objective is to be able to divide a polynomial by a monomial.

( )6 3 32x x

Step 1

( )6 3 32x x Divide each term of the polynomial by the monomial.

6

3

3

3

2x

x x

Step 2

6

3

3

3

2x

x x

Factor each expression.

2 3

3

3

3

x x

x x

Step 32 3

3

3

3

x x

x xDivide out the common factors in each expression.

2 3

3

3

3

x x

x x

The numbers and variables which are crossed out divide out to 1.

Step 4

2 3

3

3

3

x x

x xWrite in simplified form.

21

xx

1 . 8 x 3 3 2 4x x A

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

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