Which of the following is the correct factorization of the polynomial below?x3 - 12A.(x + 3)(x - 4)B.(x - 3)(x + 4)C.(x + 3)(x2 - 4x + 4)D.The polynomial is irreducible.
Question
Which of the following is the correct factorization of the polynomial below?x3 - 12A.(x + 3)(x - 4)B.(x - 3)(x + 4)C.(x + 3)(x2 - 4x + 4)D.The polynomial is irreducible.
Solution
The correct factorization of the polynomial x^3 - 12 is not listed in the options provided. This is because x^3 - 12 is a difference of cubes and can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).
In this case, a = x and b = 2∛12.
So, the correct factorization of x^3 - 12 would be (x - 2∛12)(x^2 + 2∛12*x + 4).
Therefore, none of the options A, B, C, or D are correct.
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