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

    (ii)    x^4 + x^3 + x^2 +x + 1

Answers (1)

Zero of polynomial   (x + 1)  is -1.

If  (x + 1)  is a factor of polynomial    p(x)=x^4 + x^3 + x^2 +x + 1  

Then, p(-1)  must be equal to zero 

Now,

\Rightarrow p(-1)=(-1)^4+(-1)^3+(-1)^2-1+1

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

Therefore,  (x + 1)  is not a factor of polynomial   p(x)=x^4 + x^3 + x^2 +x + 1

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