# FACTORING EXPRESSIONS

Factoring Expressions :

In this section, you will learn how to factor an algebraic expression.

## Factoring Expressions - Steps

Step 1 :

Find the largest common divisor for all the terms in the expression given.

Step 2 :

Divide each term of the expression by the largest common divisor.

Step 3:

Write the quotients inside the parentheses.

Step 4 :

Write the largest common divisor and the parentheses together using multiplication.

## Factoring Expressions - Examples

Example 1 :

Factor :

4x + 8

Solution :

Step 1 :

Find the largest common divisors for 4x and 8.

The largest common divisor for 4x and 8 is 4.

Step 2 :

Divide 4x and 8 by 4

4x / 4  =  x

8 / 4  =  2

Step 3 :

Write the quotients x and 2 inside the parentheses and multiply by the largest common divisor 4.

4(x + 2)

So,

4x + 8  =  4(x + 2)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 4 and (x+2).

Distribute 4 to x and 2.

4(x + 2)  =  4 ⋅ x + 4 ⋅ 2

4(x + 2)  =  4x + 8

When we multiply 4 and (x + 2), we get the expression given.

So, 4 and (x + 2) are the factors of 4x + 8.

Example 2 :

Factor :

16a + 64b - 4c

Solution :

Step 1 :

Find the largest common divisors for 16a, 64b and 4c.

The largest common divisor for  16a, 64b and 4c is 4.

Step 2 :

Divide 16a, 64b and 4c by 4

16a / 4  =  4a,

64b / 4  =  16b

4c / 4  =  c

Step 3 :

Write the quotients 4a, 16b and c inside the parentheses and multiply by the largest common divisor 4.

4(4a + 16b - c)

So,

16a + 64b - 4c  =  4(4a + 16b - c)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 4 and (4a + 16b - c).

Distribute 4 to 4a, 16b and c.

4(4a + 16b - c)  =  4 ⋅ 4a + 4 ⋅ 16b - 4 ⋅ c

4(4a + 16b - c)  =  16a + 64b - 4c

When we multiply 4 and (4a+16b-c), we get the expression given.

So, 4 and (4a+16b-c) are the factors of 16a + 64b - 4c.

Example 3 :

Factor :

5x2 - 15x

Solution :

Step 1 :

Find the largest common divisors for 5x2 and 15x.

The largest common divisor for 5x2 and 15x is 5x.

Step 2 :

Divide 5x2 and 15x by 5x.

5x2 / 5x  =  x

15x / 5x   =  3

Step 3 :

Write the quotients x and 3 inside the parentheses and multiply by the largest common divisor 5x.

(5x)(x - 3)

So,

5x2 + 15x  =  (5x)(x - 3)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 5x and (x - 3).

Distribute 5x to x and 3.

(5x)(x - 3)  =  5x ⋅ x - 5x ⋅ 3

(5x)(x - 3)  =  5x2 - 15x

When we multiply 5x and (x-3), we get the expression given.

So, 5x and (x-3) are the factors of  5x2 - 15x.

After having gone through the stuff given above, we hope that the students would have understood how to factor algebraic expressions.

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