Question

Please help me I will give brainlest if right

Answer 1

Given:

Consider the given polynomial is:

$x^3+4x^2+16x+64$

To find:

The complete factorization of the given polynomial.

Solution:

We have,

$x^3+4x^2+16x+64$

Using grouping method, we get

$=(x^3+4x^2)+(16x+64)$

$=x^2(x+4)+16(x+4)$

$=(x+4)(x^2+16)$

$=(x+4)(x+4i)(x-4i)$         $[\because x^2+y^2=(x+iy)(x-iy)]$

Therefore, the correct option is C.