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Find the binomial that completes the factorization.\newlinex3+8=(‾)(x2−2x+4)x^3 + 8 = (\underline{\hspace{3cm}})(x^2 - 2x + 4)

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Full solution

Q. Find the binomial that completes the factorization.\newlinex3+8=(‾)(x2−2x+4)x^3 + 8 = (\underline{\hspace{3cm}})(x^2 - 2x + 4)
  1. Factorization of x3+8x^3 + 8: We know that x3+8x^3 + 8 is a sum of cubes, which factors as (x+2)(x2−2x+4)(x + 2)(x^2 - 2x + 4).
  2. Identification of completing binomial: So, the binomial that completes the factorization is (x+2)(x + 2).

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