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

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

Answers (1)

Zero of polynomial  g(x)=x+2  is  -2

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

Then,  p(-2)  must be equal to zero 

Now,

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

\Rightarrow p(-2)= -8+12-6+1 = -1\neq 0

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

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