Question

Which of the following is the correct factorization of the polynomial below?p3 - 21603O A. (0-360)(p? + 36pq + 692)O B. (p2 + 129) (03 + 36pq + 50%)O C. (2-6)(p2 + 6pq + 3602)O D. The polynomial is irreducible.

Answer 1

We have the polynomial:

`p^3-216q^3`

We have to factorize it.

We know that 216 is the cube of 6.

We then applied the property for the difference of cubes.

`\begin{gathered} p^3-(6q)^3 \\ (p-6q)(p^2+p\cdot6q+(6q)^2) \\ (p-6q)(p^2+6pq+36q^2) \end{gathered}`

The answer is Option C.

Difference of cubes property:

x^3-y^3 = (x-y)(x^2+xy+y^2)