# Need to calculate:The factorization of 2x^{3}-8x^{2}-9x+36.

Question
Polynomial factorization
Need to calculate:The factorization of $$2x^{3}-8x^{2}-9x+36$$.

2020-11-24
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 $$2x^{3}-8x^{2}-9x+36$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$2x^{3}-8x^{2}-9x+36=(2x^{3}-8x^{2})-(9x-36)$$
$$=2x^{2}(x-4)-9(x-4)$$
As, $$(x-4)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$2x^{2}(x-4)-9(x-4)=(x-4)(2x^{2}-9)$$
Therefore, the factorization of the polynomial $$2x^{3}-8x^{2}-9x+36$$ is $$(x-4)(2x^{2}-9)$$.

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