Determine if the following polynomials has $(x+1)$ a factor:
$x^{3}+x^{2}+x+1$
Given :
The given term is $(x + 1)$
To find :
We have to check whether the polynomial $x^{3}+x^{2}+x+1$ has $(x + 1)$ as a factor.
Solution :
According to factor theorem, If $(x+1)$ is a factor of given polynomial p(X) , then at $x= -1$, p(x) will be zero.
$x^{3}+x^{2}+x+1$
Let p(x)= $x^{3}+x^{2}+x+1$
Substituting $x= -1$
$p(−1)=(−1)^3+(−1)^2+(−1)+1 =−1+1−1+1=0$
Hence, by factor theorem, $x+1$ is a factor of $x^{3}+x^{2}+x+1$.
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