Question

What is the complete factorization of the polynomial below x^3+x^2+4x+4?

Answer 1

B. 

It can first be factored by splitting to:

(x + 1)(x^2 +4)

And (x^2 + 4) splits to x +/- 2i

Answer 2

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

$x^3+x^2+4x+4$

We need to given the complete factorization of the above expression.

So, First we factorise the above expression.

$x^3+x^2+4x+4\\\\=x^2(x+1)+4(x+1)\\\\=(x+1)(x^2+4)$

Since factorization of $x^2+4$ would contain complex number.

so, it becomes,

$x^2+4=(x+2i)(x-2i)$

So, the complete factorisation would be (x+2i)(x-2i)(x+1).

Hence, Option 'B' is correct.