Question

Which of the following is the correct factorization of the polynomial below?
64x^3 + 125
A. (4x + 5)(16x^2 - 12x + 5)
B. (4x + 5)(16x^2 - 20x + 25)
C. (16x2 + 5)(5x - 16x + 125)
D. The polynomial is irreducible.

Answer 1

Hey there,

This question is purely based on Algebraic Identities .

We know that,

a³ + b³ = ( a + b) ( a² - ab + b²)

So in the same way,

64x³ + 125 = (4x)³ + 5³ is in the same form

Applying the same formula

64x³ + 125

= (4x + 5) ( 16x² - 20x + 24)

So, Option B is correct.