Question

Which of the following is the correct factorization of the polynomial below? x^3-12

Answer 1

This question is not complete.

Explanation:

Hi, The question is not complete but i think the question was this:

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

x^3 - 12

A. (x + 3)(x - 4)

B. (x - 3)(x + 4)

C. (x + 3)(x^2 - 4x + 4)

D. The polynomial is irreducible.

in which case, the answer will be this:

D as this polynomial can't be reduced

Answer 2

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

Explanation:

Question is incomplete (options are missing);

However, I'll factorize the polynomial using identity

Given

x³ - 12

This can be factorized using the following identity

a³ - b³ = (a - b)(a² + ab + b²)

By comparison,

a³ = x³ and b³ = 12

a = x and b = ∛12

Replace a with x and b with ∛12 in the above equation

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

x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

This is as far as it can be factorized

So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)