Question

Which of the following is a factor of x^15 - 64

A) x^5 - 4
B) x^10 - 4x^5 + 16
C) x^10 - 4
D) x^15 + 8x + 16​

Answer 1

A

Explanation:

`x^(15)` - 64 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Hence

`x^(15)` - 64

= (
`x^(5)`)³ - 4³

= (
`x^(5)` - 4)(
`x^(10)` + 4
`x^(5)` + 16)

Thus A is a factor