Question

question 5 of 10
which of the following is the correct factorization of the polynomial below?
$p^{3}-343q^{3}$
a. $(p - 49q)(p^{2}+7pq + 49q^{2})$
b. $(p - 7q)(p^{2}+7pq + 49q^{2})$
c. $(p^{2}+7q)(p^{3}+49pq + 7q^{2})$
d. the polynomial is irreducible.

Explanation:

Step1: Recall difference - of - cubes formula

The difference - of - cubes formula is $a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})$.

Step2: Identify $a$ and $b$

In the polynomial $p^{3}-343q^{3}$, we know that $a = p$ and since $343q^{3}=(7q)^{3}$, then $b = 7q$.

Step3: Apply the formula

Substitute $a = p$ and $b = 7q$ into the difference - of - cubes formula: $p^{3}-343q^{3}=(p - 7q)(p^{2}+7pq + 49q^{2})$.

Answer:

B. $(p - 7q)(p^{2}+7pq + 49q^{2})$