AlgebraStructure & Method · Book 1All Chapters

Factoring Patterns

5-9Factoring Pattern for ax² + bx + c

Overview

Leading coefficient ≠ 1. Use trial-and-check, grouping, or the ‘ac’ method.

Key ideas

  • Find two numbers multiplying to ac and adding to b.
  • Split the middle term and factor by grouping.
  • Always check by FOIL.

Worked examples

Example 1

Problem. Factor 2x^2 + 7x + 3.

Solution. ac = 6; numbers 6 and 1. Split: 2x^2 + 6x + x + 3 = 2x(x+3) + 1(x+3) = (2x+1)(x+3).

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Factor 3x^2 + 7x + 2.

  2. 2.

    Factor 2x^2 − 5x − 3.

  3. 3.

    Factor 6x^2 + 11x + 3.

Challenge problems

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

  1. 1.

    Factor: 2x² + 7x + 3.

  2. 2.

    Factor: 3x² − 10x + 8.