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

geduiwelh 2020-12-02 Answered
Need to calculate:The factorization of 2x3+6x2+x+3.
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Expert Answer

SoosteethicU
Answered 2020-12-03 Author has 102 answers
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,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the polynomial 2x3+6x2+x+3.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
2x3+6x2+x+3=(2x3+6x2)+(x+3)
=2x2(x+3)+1(x+3)
As, (x+3) is the common factor of the polynomial,
The polynomial can be factorized as,
2x2(x+3)+1(x+3)=(x+3)(2x2+1)
Therefore, the factorization of the polynomial 2x3+6x2+x+3 is (x+3)(2x2+1).
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