- Properties of Real Numbers
- Home
- Identifying Like Terms
- Combining like terms: Whole number coefficients
- Introduction to properties of addition
- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

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# 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 + 63n^{2}

### Solution

**Step 1:**

The HCF of 28n and 63n^{2} is 7n

**Step 2:**

Factoring the linear binomial

28n + 63n^{2} = 7n (4 + 9n)

Factor the following linear binomial:

65z – 52z^{4}

### Solution

**Step 1:**

The HCF of 65z and 52z^{4} is 13z

**Step 2:**

Factoring the linear binomial

65z – 52z^{4} = 13z (5 – 4z^{3})

Factor the following linear binomial:

24x + 84x^{3}

### Solution

**Step 1:**

The HCF of 24x and 84x^{3} is 12x

**Step 2:**

Factoring the linear binomial

24x + 84x^{3} = 12x (2 + 7x^{2})