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Factor by grouping x^3 + 2x^2 - 4x - 8

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Answer
(x−2)(x+2)2\boxed{(x - 2)(x + 2)^2}

Multiplying the factors back together yields the original polynomial x3+2x2−4x−8x^3 + 2x^2 - 4x - 8.

Problem: Factor by grouping the expression x3+2x2−4x−8x^3 + 2x^2 - 4x - 8.

Steps

  1. Group the terms
    (x3+2x2)−(4x+8)(x^3 + 2x^2) - (4x + 8)
  2. Factor out the greatest common factor from each group
    x2(x+2)−4(x+2)x^2(x + 2) - 4(x + 2)
  3. Factor out the common binomial
    (x2−4)(x+2)(x^2 - 4)(x + 2)
  4. Factor the difference of squares
    (x−2)(x+2)(x+2)(x - 2)(x + 2)(x + 2)
  5. Combine repeated factors
    (x−2)(x+2)2(x - 2)(x + 2)^2

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