Need to calculate:The factorization of x^{3}-7x^{2}+4x-28.

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 $x^3—7x^2+4x-28$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$x^3-7x^2+4x-28=(x^3-7x^2)+(4x-28)$
$=x^2(x-7)+4(x-7)$
As, $(x-7)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$x^3-7x^2+4x-28=x^2(x-7)+4(x-7)$
$=(x-7)(x^2+4)$
Therefore, the factorization of the polynomial is $(x—7)(x^2+4)$.