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

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

Question
Polynomial factorization
asked 2020-12-24
Need to calculate:The factorization of \(x^{3}+3x^2+2x+6\)

Answers (1)

2020-12-25
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 \(x^{3} + 3x^{2} + 2x + 6\).
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
\(x^{3}+3x^{2}+2x+6=(x3 + 3x^{2})+(2x+6)\)
\(=x^{2} (x+3)+2(x+3)\)
As, \((x + 3)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(x^{3}+3x^{2}+2x+6=x^{2}(x+3)+2(x+3)\)
\(=(x+3)(x^{2}+2)\)
Therefore, the factorization of the polynomial \(x^{3}+3x^{2}+2x+6\) is \((x+3)(x^{2}+2)\).
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