# Solve. The factorization of the polynomial is (3x+2)(2x^{2}+1). Given Information: The provided polynomial is 6x^{3}+4x^{2}+3x+2.

Question
Polynomial factorization
Solve. The factorization of the polynomial is $$(3x+2)(2x^{2}+1)$$.
Given Information:
The provided polynomial is $$6x^{3}+4x^{2}+3x+2$$.

2021-02-22
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 $$6x^{3}+4x^{2}+3x+2$$.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
$$6x^{3}+4x^{2}+3x+2=(6x^{3}+4x^{2})+(3x+2)$$
$$= 2x^{2}(3x+2)+1(3x+2)$$
As,$$(3x + 2)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$6x^{3}+4x^{2}+3x+2=2x^{2}(3x+2)+1(3x+2)$$
$$=(3x+2)(2x^{2}+1)$$
Therefore, the factorization of the polynomial is $$(3x+2)(2x^{2}+1)$$.

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