Question

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)
D. The polynomial is irreducible.

Answer 1

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

Answer 2

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.