Q

# Determine which of the following polynomials has (x + 1) a factor : (i) x ^3 + x ^2 + x + 1

1.(i) Determine which of the following polynomials has $(x + 1)$ a factor :

(i)    $x^3 + x^2 +x + 1$

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Zero of polynomial   $(x + 1)$  is -1.

If  $(x + 1)$  is a factor of polynomial    $p(x)=x^3 + x^2 +x + 1$

Then, $p(-1)$  must be equal to zero

Now,

$\Rightarrow p(-1)=(-1)^3+(-1)^2-1+1$

$\Rightarrow p(-1)=-1+1-1+1 = 0$

Therefore,  $(x + 1)$  is a factor of polynomial    $p(x)=x^3 + x^2 +x + 1$

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