Factoring by Grouping Math Example 2

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Example 2

hard
Factor 6x3−9x2−4x+66x^3 - 9x^2 - 4x + 6 by grouping.

Solution

  1. 1
    Step 1: Group: (6x3−9x2)+(−4x+6)(6x^3 - 9x^2) + (-4x + 6).
  2. 2
    Step 2: Factor each: 3x2(2x−3)+(−2)(2x−3)3x^2(2x - 3) + (-2)(2x - 3).
  3. 3
    Step 3: Note −4x+6=−2(2x−3)-4x + 6 = -2(2x - 3). Common binomial: (2x−3)(2x - 3).
  4. 4
    Step 4: (3x2−2)(2x−3)(3x^2 - 2)(2x - 3).
  5. 5
    Check: At x=2x = 2: (12−2)(4−3)=10(12-2)(4-3) = 10 and 6(8)−9(4)−4(2)+6=48−36−8+6=106(8)-9(4)-4(2)+6 = 48-36-8+6 = 10 ✓

Answer

(3x2−2)(2x−3)(3x^2 - 2)(2x - 3)
Sometimes you need to factor out a negative from the second group to reveal the common binomial factor. Always check that both groups produce the same binomial.

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 1 medium

Factor [formula] by grouping.

Example 3 easy

Factor [formula].

Example 4 medium

Factor [formula].

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