Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
For $x+1=0,$ we have $x=-1$.
$\therefore $ The zero of $x+1$ is $-1$.
$\because$ $p ( x ) = x ^{4}+ x ^{3}+ x ^{2}+ x +1 $
$\therefore$ $p (-1) =(-1)^{4}+(-1)^{3}+(-1)^{2}+(-1)+1$
$=1-1+1-1+1=3-2=1$
$\because$ $f (-1) \neq 0 $
$\therefore$ $p ( x )$ is not divisible by $x +1$.
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