Factoring Trinomials Worksheet

This factoring trinomials worksheet helps students practice breaking quadratic expressions into two binomial factors. The printable set includes 12 randomized questions and an answer key on page 2.

What is Factoring a Trinomial?

Factoring a trinomial means rewriting a three-term polynomial as a product of two simpler expressions. For many Algebra I problems, the goal is to find two numbers that multiply to the constant term and add to the middle coefficient.

How to Factor Trinomials

1. Check whether there is a GCF first.
2. Identify the trinomial in the form $x^2 + bx + c$ or a similar quadratic expression.
3. Find two numbers that multiply to $c$ and add to $b$.
4. Write the trinomial as a product of two binomials.

Example

Factor $x^2 + 7x + 12$

You need two numbers that multiply to $12$ and add to $7$.

Those numbers are $3$ and $4$.

So:

$x^2 + 7x + 12 = (x + 3)(x + 4)$

FAQ

Q: What should I do if I cannot find the right pair of numbers?
A: Double-check the signs and make sure the expression has been simplified fully before factoring.

Q: Do all trinomials factor over the integers?
A: No. Some trinomials are prime and do not factor nicely using integers.