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

Lipossig 2021-02-16 Answered
Need to calculate:The factorization of 8x3+20x2+2x+5.
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Expert Answer

ottcomn
Answered 2021-02-17 Author has 97 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 8x3+20x2+2x+5.
This is a four term polynomial, factorization of this polynomial can be found by factor bycgrouping as,
8x3+20x2+2x+5=(8x3+20x2)+(2x+5)
=4x2(2x+5)+1(2x+5)
As, (2x+5) is the common factor of the polynomial,
The polynomial can be factorized as,
8x3+20x2+2x+5=4x2(2x+5)+1(2x+5)
=(2x+5)(4x2+1)
Therefore, the factorization of the polynomial is (2x+5)(4x2+1).
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