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Question

Determine whether the following polynomial has (x+1) as a factor:
x4x3+x2x+1.

Solution
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To check whether (x+1) is the factor of polynomial x4x3+x2x+1:
We take, x+1=0 x=1.
Replace x by 1, we get,
p(x)=x4x3+x2x+1
p(1)=(1)4(1)3+(1)2(1)+1
p(1)=1(1)+1(1)+1=1+1+1+1+1
p(1)=5.
That is, value of p(1) is not zero.
Then x+1 is not the factor of polynomial x4x3+x2x+1.

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