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Question

Determine if the polynomial has (x+1) as a factor: x3+x2+x+1


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Solution

Factor of polynomial.

If (x+a) is a factor of a given polynomial P(x). Then, P(-a)=0 (Factor theorem)

Here, P(x)=x3+x2+x+1

Need to check if (x+1) is a factor of x3+x2+x+1 or not.

Substitute x=-1 in the given polynomial:

P(-1)=(-1)3+(-1)2+(-1)+1⇒P(-1)=-1+1-1+1⇒P(-1)=0

Hence, (x+1) is a factor of the given polynomial P(x)=x3+x2+x+1 .


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