Question

question 1 of 10
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.

Explanation:

Step1: Expand option A

$(x + 3)(x - 4)=x^{2}-4x+3x - 12=x^{2}-x - 12
eq x^{3}-12$

Step2: Expand option B

$(x - 3)(x + 4)=x^{2}+4x-3x - 12=x^{2}+x - 12
eq x^{3}-12$

Step3: Expand option C

$(x + 3)(x^{2}-4x + 4)=x^{3}-4x^{2}+4x+3x^{2}-12x + 12=x^{3}-x^{2}-8x + 12
eq x^{3}-12$

Step4: Consider irreducibility

The polynomial $x^{3}-12$ cannot be factored over the integers using simple binomial or trinomial - factoring techniques.

Answer:

D. The polynomial is irreducible.