Need to calculate:The factorization of the polynomial, 3x^{2}-2x+3x-2.

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 $3x^2—2x+3x—2$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$3x^2—2x+3x—2=(3x^2—2x)+(3x—2)$
$=x(3x-2)+1(3x-2)$
As, the binomial $(3x—2)$ is the common factor of the polynomial.
The polynomial can be factorized as,
$3x^2—2x+3x-2=x(3x—2)+1(3x-2)$
$=(3x-2)(x+1)$
Therefore, the factorization of the polynomial is $(3x—2)(x+1)$.