Factoring by Grouping Math Example 4

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

Example 4

medium
Factor 2x3−x2+8x−42x^3 - x^2 + 8x - 4.

Solution

  1. 1
    (2x3−x2)+(8x−4)=x2(2x−1)+4(2x−1)(2x^3 - x^2) + (8x - 4) = x^2(2x - 1) + 4(2x - 1).
  2. 2
    (x2+4)(2x−1)(x^2 + 4)(2x - 1).

Answer

(x2+4)(2x−1)(x^2 + 4)(2x - 1)
After grouping and factoring each pair, the common binomial (2x−1)(2x - 1) is factored out. Note x2+4x^2 + 4 cannot be factored further over the reals.

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 2 hard

Factor [formula] by grouping.

Example 3 easy

Factor [formula].

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