Practice Factoring Trinomials in Math

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

Quick Recap

Factoring a trinomial of the form ax^2 + bx + c into a product of two binomials by finding two numbers that multiply to ac and add to b.

You are reverse-engineering FOIL. If (x + p)(x + q) = x^2 + (p+q)x + pq, then you need two numbers p and q whose sum is b and whose product is c (when a = 1). When a \neq 1, use the AC method: find two numbers that multiply to ac and add to b, then split the middle term and factor by grouping.

Example 1

easy
Factor x^2 + 5x + 6.

Example 2

hard
Factor 2x^2 + 7x + 3 using the AC method.

Example 3

easy
Factor x^2 - 7x + 12.

Example 4

medium
Factor x^2 + 2x - 15.
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