The correct factorization of the polynomial p^3 - 216q^3 is C. (p - 6q)(p^2 + 6pq + 36q^2).

Here's the step-by-step process:

1. Recognize that the given polynomial is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).

2. In this case, a is p and b is (6q) because (6q)^3 = 216q^3.

3. Substitute a and b into the formula to get the factorization: (p - 6q)(p^2 + 6pq + 36q^2).

Question

The correct factorization of the polynomial p^3 - 216q^3 is C. (p - 6q)(p^2 + 6pq + 36q^2).

Here's the step-by-step process:

1. Recognize that the given polynomial is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).

2. In this case, a is p and b is (6q) because (6q)^3 = 216q^3.

3. Substitute a and b into the formula to get the factorization: (p - 6q)(p^2 + 6pq + 36q^2).

Knowee AI · Accepted Answer

The correct factorization of the polynomial p^3 - 216q^3 is C. (p - 6q)(p^2 + 6pq + 36q^2).

Here's the step-by-step process:

1. Recognize that the given polynomial is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).

2. In this case, a is p and b is (6q) because (6q)^3 = 216q^3.

3. Substitute a and b into the formula to get the factorization: (p - 6q)(p^2 + 6pq + 36q^2).

Which of the following is the correct factorization of the polynomial below?p3 - 216q3A.(p - 36q)(p2 + 36pq + 6q2)B.(p2 + 12q)(p3 + 36pq + 5q2)C.(p - 6q)(p2 + 6pq + 36q2)D.The polynomial is irreducible.SUBMITarrow_backPREVIOUS