Mixed Factoring Polynomials Worksheet

This mixed factoring polynomials worksheet combines GCF, trinomials, and difference of squares in one printable review. It includes 16 randomized questions and an answer key on page 2.

What Does This Worksheet Cover?

This worksheet is designed for mixed factoring review. Students practice deciding whether to factor out a GCF first, use trinomial factoring, or recognize a difference of squares pattern.

How to Approach Mixed Factoring Problems

1. Look for a GCF first.
2. Decide whether the remaining expression is a trinomial or a special pattern.
3. Use the factoring method that best matches the expression.
4. Check your answer by multiplying the factors back together.

Example

Factor $3x^2 - 12$

First factor out the GCF:

$3x^2 - 12 = 3(x^2 - 4)$

Then factor the difference of squares:

$3(x^2 - 4) = 3(x - 2)(x + 2)$

FAQ

Q: Why should I check for GCF first?
A: Many factoring problems are not completely factored until the GCF is removed first.

Q: How do I know which factoring method to use?
A: Start by identifying the structure of the expression: common factor, trinomial, or special product pattern.