We have been given the function [tex]x^{15}-64[/tex]
Convert this expression in difference of cubes form.
[tex]x^{15}-64\\=(x^5)^3-4^3[/tex]
Now, in order to find the factors, we can apply the difference of cubes form, which is given by
[tex]x^3-y^3=(x-y)(x^2+xy-y^2)[/tex]
On applying this formula, we get
[tex](x^5-4)(x^{10}+4x^5+16)[/tex]
Hence, the factors of the given expression are
[tex](x^5-4) \text{ and }(x^{10}+4x^5+16)[/tex]
Out of the given option, A is the correct option.
x^5 − 4 is the required factor.
