Question

Which of the following is the correct factorization of the polynomial below? 64x^3+125

Answer 1

Choice B is correct answer.

Explanation:

We have given a polynomial.

64x³+125

We have to factorize given polynomial.

We use following formula to solve it.

a³+b³ = (a+b)(a²-ab+b²)

64x³+125 = (4x)³+(5)³

Using above formula , we have

64x³+125 = (4x+5)((4x)²-(4x)(5)+(5)²)

64x³+125 = (4x+5)(16x²-20x+25) which is the answer.

Answer 2

Answer: B:
`(4x+5)(16x^2-20x+25)`

Explanation:

`a^3+b^3= (a+b)(a^2-ab+b^2)`

Thus,

`64x^3+125`

`=(4x)^3 + (5)^3`

`= (4x+5)((4x)^2-4x* 5 + (5)^2)`

`= (4x+5)(16x^2-20x+25)`

`\implies 64x^3+125=(4x+5)(16x^2-20x+25)`

⇒ Second option is correct.