question_answer

If on dividing the polynomial \[\mathbf{f(x)=}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-4}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+7x-9}\] by a polynomial g(x), the quotient q(x) and the remainder r(x) are \[(x-3)\] and \[(2x-3)\] respectively, the polynomial g(x) is ____

A)  \[{{x}^{2}}+x+1\]      

B) \[{{x}^{2}}-x+2\]

C)  \[2{{x}^{2}}+x+1\]      

D) \[2{{x}^{2}}-x+2\]

E)  None of these