Need to calculate:The factorization of x3+3x2+2x+6

Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
$ab+ac+bd+cd=a(b+c)+d(b+c)$
$=(a+d)(b+c)$
Or,
$ab—ac+bd—cd=a(b—c)+d(b-c)$
$=(a+d)(b-c)$
Calculation:
Consider the polynomial $x^3+3x^2+2x+6$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$x^3+3x^2+2x+6=(x3+3x^2)+(2x+6)$
$=x^2(x+3)+2(x+3)$
As, $(x+3)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$x^3+3x^2+2x+6=x^2(x+3)+2(x+3)$
$=(x+3)(x^2+2)$
Therefore, the factorization of the polynomial $x^3+3x^2+2x+6$ is $(x+3)(x^2+2)$.