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

Answer:

A

Step-by-step 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