Which of the following is the correct factorization of the polynomial below?p3 - 125q3A.(p - 5q)(p2 + 5pq + 25q2)B.(p - 25q)(p2 + 25pq + 25q2)C.(p2 + 10q)(p3 + 25pq + 5q2)D.The polynomial is irreducible.
Question
Which of the following is the correct factorization of the polynomial below?p3 - 125q3A.(p - 5q)(p2 + 5pq + 25q2)B.(p - 25q)(p2 + 25pq + 25q2)C.(p2 + 10q)(p3 + 25pq + 5q2)D.The polynomial is irreducible.
Solution
The correct factorization of the polynomial p^3 - 125q^3 is (p - 5q)(p^2 + 5pq + 25q^2). This is because p^3 - 125q^3 is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, a is p and b is 5q. So, the correct answer is A. (p - 5q)(p^2 + 5pq + 25q^2).
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