# Factor out the common factor

Factor out the common factor.

(5x - 2)2 + (5x - 2)

Completely factor the expression.

x4 - 3x3 + x2 - 3x

Write the rational expression in simplest form.

4x2y

xy - y

Write the rational expression in simplest form.

9x2 + 9x

8x + 8

Write the rational expression in simplest form.

x2 - 9

3 - x

Perform the multiplication and simplify.

x + 4

x3(9 - x)

· x(x - 9)

13

Perform the division and simplify.

3y - 12

8y + 24

÷ 4 - y

5y + 15

Factor the expression by removing the common factor with the smaller exponent. (Factor your answer completely.)

x5 - 3x-4

Factor the expression by removing the common factor with the smaller exponent. (Factor your answer completely.)

4x(x - 8)-6 - 12x2(x - 8)-7

Divide and simplify. See Examples 6-8.

x2 + 16

3(x + 7)

÷ x + 4

3(x2 - 49)

, x ≠ ±7

Insert the required factor in the parentheses.

3x6

4

= 3

4

( )

Insert the required factor in the parentheses.

5

7

x + 1

2

= 1

7

( )

Insert the required factor in the parentheses.

3(6x + 1)x1/2 + 4x3/2

STEP 1: Factor out x1/2.

x1/2(3( ) + )

STEP 2: Combine like terms.

x1/2(_ )

Write the following expression using negative exponents.

x + 5

x(2-x)1/3

Write the fraction as a sum of two or more terms.

x10 - 5x7 + 6

x2

Simplify the expression.

x5(-2)(x2 + 3)-4(2x) - (x2 + 3)-3(2)x4

(x5)2

Simplify the expression.

(4x - 1)1/2 - (x + 2)(4x - 1)-1/2

#### Solution Preview

Factor out the common factor.

(5x - 2)2 + (5x - 2)

Completely factor the expression.

x4 - 3x3 + x2 - 3x

Write the rational expression in simplest form.

4x2y

xy - y

Write the rational expression in simplest form.

9x2 + 9x

8x + 8

Write the rational expression in simplest form.

x2 - 9

3 - x

Perform the multiplication and simplify.

x + 4 ...

#### Solution Summary

The expert factors out the common factor.