2.(i) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

    (i)    p(x) = 2x^3 + x^2 - 2x - 1,\ g(x) = x + 1

Answers (1)

Zero of polynomial  g(x)=x+1  is  -1

If  g(x)=x+1  is factor of polynomial  p(x) = 2x^3 + x^2 - 2x - 1 

Then,  p(-1)  must be equal to zero 

Now,

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

\Rightarrow p(-1)= -2+1+2-1 = 0

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

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