Factoring by grouping

Math

Definition

Factoring by grouping is a method used to factor polynomials with four terms by grouping them into two pairs, factoring out the GCF from each pair, and then factoring out the common binomial factor.

How It Works

  1. Group the four terms into two pairs
  2. Factor out the GCF from each pair
  3. If both pairs produce the same binomial factor, factor it out
  4. Write the final factored form as a product of two binomials

Examples

  • x³ + 2x² + 3x + 6 = x²(x+2) + 3(x+2) = (x+2)(x²+3)
  • 2xy + 6x + 3y + 9 = 2x(y+3) + 3(y+3) = (y+3)(2x+3)
  • Used to factor harder trinomials like 6x² + 11x + 4 via the AC method

Related Terms

Factoring trinomials Gcf factoring Difference of squares Solving by factoring

Study This Concept

Practice factoring by grouping with free review games in these units:

Algebra 1 Unit 7: Factoring