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

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

Question
Polynomial factorization
asked 2021-01-07
Need to calculate:The factorization of \(3x^{3}+2x^{2}+3x+2\).

Answers (1)

2021-01-08
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is calledcfactor 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 \(3x^{3}+2x^{2}+3x+2\).
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
\(3x^{3}+2x^{2}+3x+2=(3x^{3}+2x^{2})+(3x +2)\)
\(=x^{2}(3x+2)+1(3x+2)\)
As, \((3x + 2)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(x^{2}(3x+2)+1(3x+2)=(3x+2)(x^{2}+1)\)
Therefore, the factorization of the polynomial \(3x^{3}+2x^{2}+3x+2\) is \((3x+2) (x^{2}+1)\).
0

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