General Factoring and Its Application
5-10Factoring by Grouping
Overview
For four-term polynomials: group in pairs, factor each pair, then factor the common binomial.
Key ideas
- Group the first two and last two terms.
- Factor out the GCF of each group.
- If the binomial factors match, factor it out.
Worked examples
Example 1
Problem. Factor x^3 + 2x^2 + 3x + 6.
Solution. x^2(x + 2) + 3(x + 2) = (x^2 + 3)(x + 2).
Practice
Try each one. Click Show answer when ready.
- 1.
Factor x^3 − 3x^2 + 2x − 6.
- 2.
Factor 2x^3 + x^2 + 4x + 2.
- 3.
Factor xy + 2x + 3y + 6.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Factor by grouping: x³ + 2x² + 3x + 6.
- 2.
Factor by grouping: 2x³ − 3x² − 4x + 6.