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

The complete factorization is (x^2 + 1)(x + 2)

Step-by-step explanation:

In order to find this, we start by splitting the 4 term polynomial into two, two-term polynomials. Then we pull out the greatest common factor of each.

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

x + 2 = 1(x + 2)

Since the remaining parentheses are identical, we use that and the two outside to factor.