Question

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

Answer 1

Answer:

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.

Answer 2

The solution of the cubic polynomials can be determined by various methods, hit and trial method is one of the best methods to find the solutions of the cubic polynomial. The complete factorization of polynomial $x^3+2x^2+ x + 2$ is $(x^2 + 1)(x + 2)$.

The given polynomial is $x^3+2x^2+ x + 2$.

Taking common factors from the polynomial and solving it further.

$\begin{aligned} x^3+2x^2+ x + 2&= (x^3+2x^2)+ (x + 2)\\&=x^2(x+2)+1(x+2)\\&=(x^2+1)(x+2) \end{aligned}$

Thus,

The complete factorization of polynomial $x^3+2x^2+ x + 2$ is $(x^2 + 1)(x + 2)$.

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