What is the complete factorization of the polynomial below ?

(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).

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