# Need to calculate:The factorization of 3p^{3}-2p^{2}-9p+6.

Need to calculate:The factorization of $3{p}^{3}-2{p}^{2}-9p+6$.
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Fatema Sutton
Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,
$ab+ac+bd+cd=a\left(b+c\right)+d\left(b+c\right)$
$=\left(a+d\right)\left(b+c\right)$
Or,
$ab-ac+bd-cd=a\left(b-c\right)+d\left(b-c\right)$
$=\left(a+d\right)\left(b-c\right)$
Calculation:
Consider the polynomial $3{p}^{3}-2{p}^{2}-9p+6$.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
$3{p}^{3}-2{p}^{2}-9p+6=\left(3{p}^{3}-2{p}^{2}\right)+\left(-9p+6\right)$
$={p}^{2}\left(3p-2\right)-3\left(3p-2\right)$
As, $\left(3p-2\right)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$3{p}^{3}-2{p}^{2}-9p+6={p}^{2}\left(3p-2\right)—3\left(3p-2\right)$
$=\left(3p-2\right)\left({p}^{2}-3\right)$
Therefore, the factorization of the polynomial is $\left(3p-2\right)\left({p}^{2}—3\right)$.