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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Updated on: 10-Oct-2022

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