Need to calculate:The factorization of x^{3}+4x^{2}+3x+12.

Formula used:
The factors of a polynomial can be found 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 $x^3+4x^2+3x+12$.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
$x^3+4x^2+3x+12=(x^3+4x^2)+(3x+12)$
$=x^2(x+4)+3(x+4)$
As, $(x+4)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$x^3+4x^2+3x+12=x^2(x+4)+3(x+4)$
$=(x+4)(x^2+3)$
Therefore, the factorization of the polynomial $x^3+4x^2+3x+12$ is $(x+4)(x^2+3)$.