# Factoring a linear binomial

To factor a number means to write it as a product of its factors.

A linear binomial has two terms and highest degree of one

For example: 2x + 1; 9y + 43; 34p + 17q are linear binomials.

To factor a linear binomial means to write it as a product of its factors.

Rules to factor a linear binomial

• At first, we find the highest common factor of the terms of the linear binomial

• The HCF is factored out and the sum/difference of remaining factors is written in a pair of parentheses.

• This is like reversing the distributive property of multiplication.

Factor the following linear binomial:

28n + 63n2

### Solution

Step 1:

The HCF of 28n and 63n2 is 7n

Step 2:

Factoring the linear binomial

28n + 63n2 = 7n (4 + 9n)

Factor the following linear binomial:

65z – 52z4

### Solution

Step 1:

The HCF of 65z and 52z4 is 13z

Step 2:

Factoring the linear binomial

65z – 52z4 = 13z (5 – 4z3)

Factor the following linear binomial:

24x + 84x3

### Solution

Step 1:

The HCF of 24x and 84x3 is 12x

Step 2:

Factoring the linear binomial

24x + 84x3 = 12x (2 + 7x2)