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

Question
Polynomial factorization
asked 2021-02-21
Solve. The factorization of the polynomial is \((3x+2)(2x^{2}+1)\).
Given Information:
The provided polynomial is \(6x^{3}+4x^{2}+3x+2\).

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 \(6x^{3}+4x^{2}+3x+2\).
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
\(6x^{3}+4x^{2}+3x+2=(6x^{3}+4x^{2})+(3x+2)\)
\(= 2x^{2}(3x+2)+1(3x+2)\)
As,\((3x + 2)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(6x^{3}+4x^{2}+3x+2=2x^{2}(3x+2)+1(3x+2)\)
\(=(3x+2)(2x^{2}+1)\)
Therefore, the factorization of the polynomial is \((3x+2)(2x^{2}+1)\).
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