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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case: (iii) p(x) = x ^3 - 4x ^2 + x + 6, g(x) = x - 3

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

   (iii)    p(x) = x^3 - 4x^2 + x + 6, \ g(x) = x - 3

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Zero of polynomial  g(x)=x-3  is  3

If  g(x)=x-3  is factor of polynomial  p(x) = x^3 - 4x^2 + x + 6 

Then,  p(3)  must be equal to zero 

Now,

\Rightarrow p(3) = (3)^3 - 4(3)^2 + 3 + 6

\Rightarrow p(3) = 27-36+3+6=0

Therefore,  g(x)=x-3   is a factor of polynomial  p(x) = x^3 - 4x^2 + x + 6

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