Solve the factorization of x^{12}+x^{7}+x^{5}+1

Kye 2020-11-02 Answered
Solve the factorization of x12+x7+x5+1
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Expert Answer

Jaylen Fountain
Answered 2020-11-03 Author has 170 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 x12+x7+x5+1.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
x12+x7+x5+1=(x12+x7)(x5+1)
=x7(x5+1)+1(x5+1)
As, (x5+1) is the common factor of the polynomial,
The polynomial can be factorized as,
x7(x5+1)+1(x5+1)=(x5+1)(x7+1)
Therefore, the factorization of the polynomial x12+x7+x5+1 is (x5+1)(x7+1).
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