Given:
Consider the given polynomial is:
[tex]x^3+4x^2+16x+64[/tex]
To find:
The complete factorization of the given polynomial.
Solution:
We have,
[tex]x^3+4x^2+16x+64[/tex]
Using grouping method, we get
[tex]=(x^3+4x^2)+(16x+64)[/tex]
[tex]=x^2(x+4)+16(x+4)[/tex]
[tex]=(x+4)(x^2+16)[/tex]
[tex]=(x+4)(x+4i)(x-4i)[/tex] [tex][\because x^2+y^2=(x+iy)(x-iy)][/tex]
Therefore, the correct option is C.
