# Intermediate Algebra Skill-Builder _ AE - 10 Dividing Polynomials

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```					Intermediate Algebra
Skill-Builder # AE - 10
Dividing Polynomials Using Long Division

Arrange both dividend and divisor in descending order. Supply any missing term by using a
coefficient of zero.

Examples

1.   (x + x     3
)
− 5 ÷ (3 + x )
Solution:
Rearrange and rewrite the dividend as x 3 + 0x 2 + x − 5 and rewrite the divisor as
x + 3 . Apply the Divide-Multiply-Subtract-Bring down process:

x 2 − 3 x + 10
x + 3 x 3 + 0x 2 + x − 5

(
− x3 + 3x 2             )
− 3x 2 + x
(
− −3 x 2 − 9 x                    )
10 x − 5
− (10 x + 30 )
− 35

35
(                         )
Thus, we get x + x 3 − 5 ÷ ( 3 + x ) = x 2 − 3 x + 10 −
x+3
.

2.   (x   4
)
− 16 y 4 ÷ ( x − 2 y )
Solution:
Rewrite the dividend as x 4 + 0x 3 y + 0x 2 y2 + 0xy3 − 16 y 4 (descending in x and
ascending in y).

x 3 + 2 x 2 y + 4 xy 2 + 8 y 3
4             3
x − 2y x + 0x y + 0x 2 y2 + 0xy3 − 16 y 4

(
− x 4 − 2x 3 y                   )
2x 3 y + 0 x 2 y 2
(
− 2x 3 y − 4 x 2 y 2                     )
2    2
4x y           + 0 xy 3
(
− 4 x 2 y 2 − 8 xy 3              )
8 xy 3 − 16 y 4
(
− 8 xy 3 − 16 y 4        )
0
Intermediate Algebra
Skill-Builder # AE - 10
Dividing Polynomials Using Long Division

Divide using long division.

1.   (x   3
)
+ x 2 + x + 1 ÷ ( x − 1)         2.   ( x − 2x    2
)
+ x 4 + 4 ÷ ( x + 2)

3.   (1 − x − x     3
) (
− x5 ÷ 1+ x + x2   )   4.   (x   3
)
+ 81y 3 ÷ ( x + 3 y )
Intermediate Algebra
Skill-Builder # AE - 10
Dividing Polynomials Using Long Division
1.
2.
3.
4.

Prepared by: Dr. Teresa V. Sutcliffe, Winter 2010

```
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