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