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

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

Question
Polynomial factorization
asked 2021-02-21
Need to calculate:The factorization of \(2z^{3}+8z^{2}+5z+20\).

Answers (1)

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 \((z+4) (2z^{2}+5)\).
0

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