Answer:
This question is not complete.
Step-by-step 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:
x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)
Step-by-step 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)
