Question

How do you factor `x^15 - 1/64`?

Answer 1

`x^15-1/64=(x^5-1/4)(x^(10)+1/4x^5+1/16)`

Explanation:

`x^15-1/64=(x^5)^3-(1/4)^3` and hence using identity

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

`(x^5)^3-(1/4)^3=(x^5-1/4)((x^5)^2+1/4x^5+(1/4)^2)`

= `(x^5-1/4)(x^(10)+1/4x^5+1/16)`