Determine which of the following polynomials has $(x + 1)$ a factor : $x^{3}+x^{2}+x+1$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{3}+x^{2}+x+1$.
For $x+1=0,$ we have $x=-1$.
$\therefore $ The zero of $x+1$ is $-1$.
$p(x)=x^{3}+x^{2}+x+1$
$\therefore $ $p(-1)=(-1)^{3}+(-1)^{2}+(-1)+1=-1+1-1+1=0$
i.e. when $p ( x )$ is divided by $( x +1),$ then the remainder is zero.
$\therefore (x+1)$ is a factor of $x^{3}+x^{2}+x+1$.
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