Practice Factoring Out the GCF in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Factoring out the greatest common factor (GCF) means identifying the largest expression that divides every term, then rewriting the polynomial as that GCF times what remains.

Look at what all terms share in common—like taking the common ingredient out of a recipe. In 6x^3 + 9x^2, every term has at least 3x^2 in it, so pull it out front: 3x^2(2x + 3).

Example 1

easy
Factor 6x^2 + 9x.

Example 2

medium
Factor 12x^3 - 8x^2 + 4x.

Example 3

easy
Factor 10x + 15.

Example 4

hard
Factor -18x^4y^2 + 12x^3y^3 - 6x^2y.
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