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

Question
Polynomial factorization asked 2020-12-02
Need to calculate:The factorization of $$2x^{3}+6x^{2}+x+3$$.

## Answers (1) 2020-12-03
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 $$2x^{3}+6x^{2}+x+3$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$2x^{3}+6x^{2}+x+3=(2x^{3}+6x^{2})+(x+ 3)$$
$$= 2x^{2}(x+3)+1(x+3)$$
As, $$(x+3)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$2x^{2}(x+3)+1(x+3)=(x+3) (2x^{2}+1)$$
Therefore, the factorization of the polynomial $$2x^{3} + 6x^{2}+x+3$$ is $$(x + 3) (2x^{2}+1)$$.

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