Question

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

Answer 1

C

Explanation:

p³ - 216q³ ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

p³ - 216q³

= p³ - (6q)³

= (p - 6q)(p² + 6pq + 36q²) → C

Answer 2

C. (p - 6q)(p² + 6pq + 36q²)

Explanation:

Equation at the end of step 1

Trying to factor as a Difference of Cubes:

Factoring: p^3 - 216q^3

Theory: A difference of two perfect cubes, a^3 - b^3 can be factored into

(a-b) • (a^2 +ab +b^2)

Proof:

Check: 216 is the cube of 6

Check: p^3 is the cube of p^1

Check: q^3 is the cube of q^1

Factorization is:

Trying to factor a multi variable polynomial :

Factoring: p^2 + 6pq + 36q^2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final Result:

(p - 6q)(p² + 6pq + 36q²)