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Find the binomial that completes the factorization.\newlinep3−1=(‾)(p2+p+1)p^3 - 1 = (\underline{\hspace{3cm}})(p^2 + p + 1)

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Full solution

Q. Find the binomial that completes the factorization.\newlinep3−1=(‾)(p2+p+1)p^3 - 1 = (\underline{\hspace{3cm}})(p^2 + p + 1)
  1. Factorization of p3−1p^3 - 1: We know that p3−1p^3 - 1 is a difference of cubes, which factors as (p−1)(p2+p+1)(p - 1)(p^2 + p + 1).
  2. Identification of completing binomial: So, the binomial that completes the factorization is (p−1)(p - 1).

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