#### What is a Trinomial?

A trinomial is a polynomial with 3 terms.. This page will focus on quadratic trinomials. The degree of a quadratic trinomial must be '2'. In other words, there must be an exponent of '2' and that exponent must be the greatest exponent.

**Examples of Quadratic Trinomials:**

$$ 3x^2 + 2x + 1$$ |

$$ 7 x^2 + 4x + 4$$ |

$$5 x^2 + 6x + 9$$ |

__Non__-Examples of Quadratic Trinomials:**Note:**For the rest of this page, 'factoring trinomials' will refer to factoring 'quadratic trinomials' . (The only difference being that a quadratic trinomial has a degree of 2.)

**Video Tutorial**

on Factoring Trinomials

**Formula** For Factoring Trinomials

(when a =1)

It's always easier to understand a new concept by looking at a specific example so you might want to do that first. This formula works when 'a' is 1. In other words, we will use this approach whenever the coefficient in from of x^{2} is 1. (If you need help factoring trinomials when $$a \ne 1 $$, then go here.

- identify a,b, and c in the trinomial ax
^{2}+ bx+c - write down all factor pairs of c
- identify which factor pair from the previous step sums up to b
- Substitute factor pairs into two binomials

**Example** of Factoring a Trinomial

##### Example 1

Factor x^{2} + 5x + 4

Identify a,b, and c in the trinomial

ax^{2} + bx+c

a=
1

b=
5

c=
4

Write down all factor pairs of 4

(Note: since 5 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positive. As the chart on the right shows you -2*-2 is positive 4...so we do have to consider these two negative factors. This is probably easier to understand if you watch our video lesson factoring trinomials)

identify which factor pair from the previous step sums up to c

If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

^{2}+ 5x + 4