show that (x-3) is a factor of the polynomial x^3-3x^2+4x-12 .

Answers (1)

solution: Let p(x)=x^3-3x^2+4x-12  be the given polynomial. By factor theorem, 

                (x-a)  is a factor of a polynomial p(x)=0 . therefore, in order to prove that  (x-3)

               is a factor of p(x) , it is sufficient to show that p(3) = 0 .

Now ,            p(x)=x^3-3x^2+4x-12

Rightarrow                  p(3)=3^3-3	imes3^2+4	imes3-12 =27-27+12-12=0

Hence , (x-3) is a factor of p(x)=x^3-3x^2+4x-12.

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