Factoring Polynomials by Grouping
Factor polynomials by grouping in Grade 9 algebra: split four terms into pairs, factor GCF from each pair, then factor out the common binomial to rewrite as a product of two binomials.
Key Concepts
New Concept When a polynomial has four terms, make two groups and factor out the greatest common factor from each group. What’s next Next, you’ll apply this method to factor polynomials with four terms and then extend the technique to trinomials by rewriting them.
Common Questions
What is polynomial factoring by grouping?
Grouping is a factoring method for four-term polynomials. Split the four terms into two pairs, factor the GCF from each pair, and if the resulting binomials match, factor that common binomial out of both groups.
How do you factor x³ + 2x² + 3x + 6 by grouping?
Group: (x³ + 2x²) + (3x + 6). Factor GCF from each: x²(x + 2) + 3(x + 2). Both groups share the factor (x + 2), so factor it out: (x + 2)(x² + 3).
What if the binomials don't match after grouping?
Try rearranging the terms into different pairs and group again. Sometimes terms need to be reordered before grouping works. If no arrangement works, the polynomial may not be factorable by grouping.