AlgebraStructure & Method · Book 1All Chapters

General Factoring and Its Application

5-11Using Several Methods of Factoring

Overview

Always start by factoring out a GCF. Then look for special patterns, then a trinomial pattern, then grouping.

Key ideas

  • GCF first, always.
  • Difference of squares? Perfect-square trinomial?
  • Factor completely — check each factor.

Worked examples

Example 1

Problem. Factor 3x^3 − 12x.

Solution. 3x(x^2 − 4) = 3x(x − 2)(x + 2).

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Factor 5x^2 − 45.

  2. 2.

    Factor 2x^2 − 8x + 8.

  3. 3.

    Factor 4x^3 − 4x.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Factor completely: 3x³ − 12x.

  2. 2.

    Factor completely: x⁴ − 16.