Dividing Polynomials

Chapter 4.6

5 – –

15y4 – 27y3 – 21y2

3y2

153 –

273 –

213

y2 y9 7

1. Divide.

y4

y2 y2

y3

y2

y2

Write as separate fractions.

Simplify each.

–( ) x3

–( )

(x3 + 10x2 + 31x + 25) ÷ (x + 4)

x )x3

x

x2

x3

6x2 + 31x

6x2

x

+ 6x

6x2

7x + 25

7xx

+ 7

–( )

7x-3

x2 + 6x + 7 x + 43

+ 4x2

+ 24x

+ 28

–

+ 10x2 + 31x + 25+ 4

2. Divide.

Divide first terms.

Multiply.

Subtract.

Bring down next term.

Write as long division.

–( ) 2x3

–( )

(2x3 – x2 + 1) ÷ (x – 1)

x )2x3

x

2x2

2x3

x2 + 0x

x2

x

+ x

x2

x + 1

xx

+ 1

–( )

x2

2x2 + x + 1 x – 12

– 2x2

– x

– 1

+

– x2 + 0x + 1– 1

3. Divide.

Divide first terms.

Multiply.

Subtract.

Bring down next term.

Write as long division.

Write 0x for the missing term.

–( ) 20x3

–( )

(20x3 – 11x2 – 11x + 6) ÷ (4x – 3)

4x )20x3

4x

5x2

20x3

4x2 – 11x

4x2

4x

+ x

4x2

-8x + 6

-8x4x

– 2

–( )-8x

5x2 + x – 2

– 15x2

– 3x

+ 6

– 11x2 – 11x + 6– 3

Divide first terms.

Multiply.

Subtract.

Bring down next term.

Write as long division.

4. Divide and check.

(20x3 – 11x2 – 11x + 6) ÷ (4x – 3)

5x2 + x – 2

4. Divide and check.

Check by multiplying the quotient and dividend.

20x3

+ 6+ 4x2 – 8x– 15x2 – 3x20x3

– 11x2 – 11x + 6

Multiply each term then combine.

( )( )5x2 + x – 2 4x – 3

√

Dividing Polynomials

Chapter 4.6