**Factoring expressions worksheet :**

Worksheet on factoring expressions is much useful to the students who are at the initial stage of learning Algebra in Math.

Before we look at the worksheet, let us look at the steps involved in factoring expressions.

**Step 1 : **

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

**Step 2 : **

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

**Step 3: **

Write the quotients inside the parenthesis.

**Step 4 : **

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

1. Factor : 4x + 8

2. Factor : 16a + 64b - 4c

3. Factor : 5x² - 15x

**Problem 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 and 8 / 4 = 2

**Step 3 :**

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

4(x + 2)

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

**Problem 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 and 4c / 4 = c

**Step 3 :**

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

4(4a + 16b - c)

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

**Problem 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 and 15x / 5x = 3

**Step 3 :**

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

(5x)(x - 3)

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

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