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

Lipossig 2021-02-21 Answered
Need to calculate:The factorization of 2z3+8z2+5z+20.
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Expert Answer

Clara Reese
Answered 2021-02-22 Author has 120 answers
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,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the polynomial 2z3+8z2+5z+20.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
2z3+8z2+5z+20=(2z3+8z2)+(5z+20)
=2z2(z+4)+5(z+4)
As, (z+4) is the common factor of the polynomial,
The polynomial can be factorized as,
2z3+8z2+5z+20=2z2(z+4)+5(z+4)
=(z+4)(2z2+5)
Therefore, the factorization of the polynomial is (z+4)(2z2+5).
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