Question

Which of the following is the correct factorization of the polynomial below?

p³ -343q³
A. (p-49q) (p² +7pq+49q²)
B. (p-7q) (p² +7pq+49q²)
C. (p² +7q) (p³ +49pq+7q²)
D. The polynomial is irreducible.

Answer 1

B

Explanation:

a difference of cubes factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

given

p³ - 343q³

= p³ - (7q)³ ← a difference of cubes , then

= (p - 7q)(p² + 7pq + 49q²) ← in factored form