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

Question
Polynomial factorization
Need to calculate:The factorization of $$3x^{3}+2x^{2}+3x+2$$.

2021-01-08
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is calledcfactor 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 $$3x^{3}+2x^{2}+3x+2$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$3x^{3}+2x^{2}+3x+2=(3x^{3}+2x^{2})+(3x +2)$$
$$=x^{2}(3x+2)+1(3x+2)$$
As, $$(3x + 2)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$x^{2}(3x+2)+1(3x+2)=(3x+2)(x^{2}+1)$$
Therefore, the factorization of the polynomial $$3x^{3}+2x^{2}+3x+2$$ is $$(3x+2) (x^{2}+1)$$.

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