Solve. The factorization of the polynomial is (3x+2)(2x^{2}+1). Given Information: The provided polynomial is 6x^{3}+4x^{2}+3x+2.

Khaleesi Herbert 2021-02-21 Answered
Solve. The factorization of the polynomial is (3x+2)(2x2+1).
Given Information:
The provided polynomial is 6x3+4x2+3x+2.
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Expert Answer

crocolylec
Answered 2021-02-22 Author has 100 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 6x3+4x2+3x+2.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
6x3+4x2+3x+2=(6x3+4x2)+(3x+2)
=2x2(3x+2)+1(3x+2)
As,(3x+2) is the common factor of the polynomial,
The polynomial can be factorized as,
6x3+4x2+3x+2=2x2(3x+2)+1(3x+2)
=(3x+2)(2x2+1)
Therefore, the factorization of the polynomial is (3x+2)(2x2+1).
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