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Find the quadratic polynomial that completes the factorization.\newlinep3−64=(p−4)(_____)p^3 - 64 = (p - 4)(\_\_\_\_\_)

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Full solution

Q. Find the quadratic polynomial that completes the factorization.\newlinep3−64=(p−4)(_____)p^3 - 64 = (p - 4)(\_\_\_\_\_)
  1. Recognize Cubic Difference: Recognize that p3−64p^3 - 64 is a difference of cubes.\newlineCalculation: p3−64p^3 - 64 can be factored as (p−4)(p2+4p+16)(p - 4)(p^2 + 4p + 16).
  2. Factorization Calculation: Match the factored form to the given partial factorization.\newlineCalculation: The quadratic polynomial that completes the factorization is p2+4p+16p^2 + 4p + 16.

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