Need to calculate:The factorization of 2x^{3}+6x^{2}+x+3.

Need to calculate:The factorization of 2x^{3}+6x^{2}+x+3.

Question
Polynomial factorization
asked 2020-12-02
Need to calculate:The factorization of \(2x^{3}+6x^{2}+x+3\).

Answers (1)

2020-12-03
Formula used:
The factors of a polynomial can be find 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 \(2x^{3}+6x^{2}+x+3\).
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
\(2x^{3}+6x^{2}+x+3=(2x^{3}+6x^{2})+(x+ 3)\)
\(= 2x^{2}(x+3)+1(x+3)\)
As, \((x+3)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(2x^{2}(x+3)+1(x+3)=(x+3) (2x^{2}+1)\)
Therefore, the factorization of the polynomial \(2x^{3} + 6x^{2}+x+3\) is \((x + 3) (2x^{2}+1)\).
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