Need to calculate:The factorization of the polynomial a^{2}+ac+a+c

ediculeN 2020-10-28 Answered
Need to calculate:The factorization of the polynomial a2+ac+a+c
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Expert Answer

curwyrm
Answered 2020-10-29 Author has 87 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 a2+ac+a+c.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
a2+ac+a+c=(a2+ac)+(a+c)
=a(a+c)+(a+c)
As, (a+c) is the common factor of the polynomial factor it out as follows:
a2+ac+a+c=a(a+c)+(a+c)
=(a+c)(a+1)
The factorization of the polynomial a2+ac+a+c is (a+c)(a+1).
Check the result as follows:
(a+c)(a+1)=aa+a1+ca+c1
=a2+ac+a+c
Thus, the factorization of the polynomial a2+ac+a+c  is (a+c)(a+1).

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