How to Factor a Simple Trinomial

Some algebraic equations are factorable. Meaning they can be represented as a multiplication of variables and constants.

There are various factoring methods, depending on what type of algebraic equation you are dealing with.

In this "How To", we'll be learning how to factor a simple trinomial.

A simple trinomial is defined as an algebraic expression consisting of three terms: x² + bx + c. The distinguishing factor of a simple trinomial is that the coefficient on the x² term is 1.

To factor a simple trinomial, we need to determine two numbers. These numbers need to add to the b-value and multiply to the c-value in the algebraic expression.

Once the two numbers are found, the rest of the factoring is easy. All we need to do is place the numbers in the factored form: y = (x+n₁)(x+n₂).

Examples

Example 1: Factor x² + 5x + 6.

Step 1: Find two numbers that add to 5 and multiply to 6

n₁ + n₂ = 5

n₁ x n₂ = 6

n₁ = 2; n₂ = 3

Step 2: Place the numbers in the factored form

y = (x+n₁)(x+n₂)

y = (x+2)(x+3)

Example 2: Factor x² - 6x + 9.

Step 1: Find two numbers that add to 5 and multiply to 6

n₁ + n₂ = -6

n₁ x n₂ = 9

n₁ = -3; n₂ = -3

Step 2: Place the numbers in the factored form

y = (x+n₁)(x+n₂)

y = (x-3)(x-3) = (x-3)²

Example 3: Factor x² + x - 20.

Step 1: Find two numbers that add to 5 and multiply to 6

n₁ + n₂ = 1

n₁ x n₂ = -20

n₁ = 5; n₂ = -4

Step 2: Place the numbers in the factored form

y = (x+n₁)(x+n₂)

y = (x+5)(x-4)