Question

What is the complete factorization of the polynomial below?
x3 + x2 + 9x+9

Answer 1

(x+1)(x-3i) (x+3i)

Explanation:

x^3 + x^2 + 9x+9

We will use factor by grouping

Factor out x^2 from the first group and 9 from the second group

x^3 + x^2 + 9x+9

x^2( x+1) + 9(x+1)

Factor out (x+1)

(x+1) ((x^2+9)

Now factor x^2+9

x^2 -(3i)^2 = (x-3i) (x+3i)

Replacing this

(x+1)(x-3i) (x+3i)