Factoring by Grouping
Group four terms in pairs and factor each pair.
About this topic
Factoring by grouping works on four-term polynomials. Split them into two pairs, factor the GCF out of each pair, and hopefully a common binomial factor appears which you then factor out. For x³ + 3x² + 2x + 6 you get x²(x + 3) + 2(x + 3) = (x + 3)(x² + 2).
If the binomials in the two groups do not match, try rearranging the terms or factoring out a negative from the second pair. For ax + ay − bx − by, group as a(x + y) − b(x + y) = (a − b)(x + y). Grouping is also the final step of the ac method for trinomials: split the middle term into two pieces, then group.
This technique is useful for factoring higher-degree polynomials and finding all roots of cubic equations in algebra and precalculus. It trains a flexible way of seeing structure in expressions, which is also used in simplifying formulas in physics and finance.
The usual errors are sign mistakes when factoring from the second pair, such as writing 2x − 6 as 2(x + 3). Factor out a negative to keep the binomials identical. If no arrangement makes a match, the polynomial may not factor by this method. Always multiply back to check.
Key ideas
- Factor the GCF from each pair
- Look for a common binomial
- Factor it out
Quick check
Use cases: where Factoring by Grouping helps
- Homework: review the key idea behind Factoring by Grouping before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Factoring by Grouping without notes.
- Visual learning: play with the interactive lab to see how Factoring by Grouping changes when you adjust its inputs.
- Teaching a friend: explain Factoring by Grouping in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Factoring by Grouping?
Group four terms in pairs and factor each pair.
What will I learn in Factoring by Grouping?
Factor the GCF from each pair. Look for a common binomial. Factor it out.
Is Factoring by Grouping part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Factoring by Grouping lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Factoring by Grouping?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.