Question

What is the complete factorization of the polynomial below ?

Answer 1

Answer:

(x - 2i)(x + 2i)(x + 1)

Step-by-step explanation:

Factor x³ + x² + 4x + 4.

Note that x² is common to the first two terms, and that 4 is common to the last two terms.

Thus:  x³ + x² + 4x + 4 = x²(x + 1) + 4(x + 1).

We see that x + 1 is common to both terms.  Thus, we have:

(x² + 4)(x + 1).  

Note that x² + 4 has two imaginary roots:  2i and -2i.  Thus, the complete

factorization of the polynomial is (x - 2i)(x + 2i)(x + 1).

Answer 2

Answer:

$(x+1)(x+2i)(x-2i)$

Step-by-step explanation:

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

Factor the given polynomial

Group first two terms and last two terms

$(x^3+x^2)+(4x+4)$

Factor out GCF from each group

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

Factor out x+1

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

Now factor out x^2+4 that is x^2  + 2^2

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

$(x+1)(x+2i)(x-2i)$