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

64x3 + 27

A(16x + 8)(3x2 - 12x + 9)
B(4x + 3)(16x2 - 12x + 9)
C(3x2 + 4)(3x - 16x + 16)
DThe polynomial is irreducible.

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taylortuanquin taylortuanquin · Answer 1 · 2017-03-17T19:43:48-04:00

64x^3 + 27 is a sum of cubes: (4x)^3 + 3^3, for which the factors are (4x + 3)(16x^2 - 12x + 9)

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ColinJacobus ColinJacobus · Answer 2 · 2019-06-29T01:29:25-04:00

Answer: the correct option is

(B) \((4x+3)(16x^2-12x+9).\)

Step-by-step explanation: We are given to select the correct factorization of the following polynomial :

\(P=64x^3+27.\)

We will be using the following factorization formula :

\(a^3+b^3=(a+b)(a^2-ab+b^2).\)

Therefore, the factorization of the given polynomial is as follows :

\(P\\\\=64x^3+27\\\\=(4x)^3+3^3\\\\=(4x+3)((4x)^2-4x\times3+3^2)\\\\=(4x+3)(16x^2-12x+9).\)

Thus, the required factored form is \((4x+3)(16x^2-12x+9).\)

Option (B) is CORRECT.