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

Question
Polynomial factorization
Need to calculate:The factorization of $$x^{3}+3x^2+2x+6$$

2020-12-25
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 $$x^{3} + 3x^{2} + 2x + 6$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$x^{3}+3x^{2}+2x+6=(x3 + 3x^{2})+(2x+6)$$
$$=x^{2} (x+3)+2(x+3)$$
As, $$(x + 3)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$x^{3}+3x^{2}+2x+6=x^{2}(x+3)+2(x+3)$$
$$=(x+3)(x^{2}+2)$$
Therefore, the factorization of the polynomial $$x^{3}+3x^{2}+2x+6$$ is $$(x+3)(x^{2}+2)$$.

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