Need to calculate:The factorization of 6z^{3}+3z^{2}+2z+1.

babeeb0oL 2021-02-14 Answered
Need to calculate:The factorization of 6z3+3z2+2z+1.
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Expert Answer

SchulzD
Answered 2021-02-15 Author has 83 answers
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,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the polynomial 6z3+3z2+2z+1.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
6z3+3z2+2z+1=(6z3+3z2)+(2z+1)
=3z2(2z+1)+1(2z+1)
As, (2z+1) is the common factor of the polynomial,
The polynomial can be factorized as,
6z3+3z2+2z+1=3z2(2z+1)+1(2z+1)
=2z+1)(3z2+1)
Therefore, the factorization of the polynomial is (2z+1)(3z2+1).
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