Question

Which of the following is the correct factorization of the polynomial below: p^3 - 216?

A. (p-6)(p^2 + 6p + 36)
B. (p^2 + 12)(p + 18)
C. (p-6)(p^2 + 6p + 36)
D. The polynomial is irreducible.

Answer 1

The polynomial p^3 - 216 is a difference of cubes and its correct factorization is (p-6)(p^2 + 6p + 36), representing option A.

Step-by-step explanation:

The correct factorization of the polynomial p^3 - 216 can be determined by recognizing that it represents a difference of cubes. A difference of cubes can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, we can let a = p and b = 6, since 6^3 = 216. Substituting a and b into the formula, we get the factorization:

p^3 - 6^3 = (p - 6)(p^2 + 6p + 36)

Therefore, the correct factorization among the given options is A. (p-6)(p^2 + 6p + 36).