Factoring by Grouping Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
Factor x3+3x2+2x+6x^3 + 3x^2 + 2x + 6 by grouping.

Solution

  1. 1
    Step 1: Group into pairs: (x3+3x2)+(2x+6)(x^3 + 3x^2) + (2x + 6).
  2. 2
    Step 2: Factor each group: x2(x+3)+2(x+3)x^2(x + 3) + 2(x + 3).
  3. 3
    Step 3: Factor out the common binomial: (x2+2)(x+3)(x^2 + 2)(x + 3).
  4. 4
    Check: (x2+2)(x+3)=x3+3x2+2x+6(x^2+2)(x+3) = x^3 + 3x^2 + 2x + 6 ✓

Answer

(x2+2)(x+3)(x^2 + 2)(x + 3)
Factoring by grouping works when pairs of terms share a common factor and the remaining binomial is the same in each group. The shared binomial becomes one factor.

About Factoring by Grouping

A factoring technique for polynomials with four or more terms: group terms into pairs, factor the GCF from each pair, then factor out the common binomial factor.

Learn more about Factoring by Grouping →

More Factoring by Grouping Examples

Example 2 hard

Factor [formula] by grouping.

Example 3 easy

Factor [formula].

Example 4 medium

Factor [formula].

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