# Need to calculate:The factorization of 2z^{3}+8z^{2}+5z+20.

Question
Polynomial factorization
Need to calculate:The factorization of $$2z^{3}+8z^{2}+5z+20$$.

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 $$2z^{3}+8z^{2}+5z+20$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$2z^{3}+8z^{2}+5z+20 = (2z^{3}+8z^{2})+(5z+20)$$
$$=2z^{2}(z+4)+5(z+4)$$
As, $$(z+4)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$2z^{3}+8z^{2}+5z+20 = 2z^{2}(z+4)+5(z+4)$$
$$=(z+4) (2z^{2}+5)$$
Therefore, the factorization of the polynomial is $$(z+4) (2z^{2}+5)$$.

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