Đáp án đúng: D
Giải chi tiết:Ta có:
\(\begin{array}{l}f\left( x \right) = {x^4} - 3{x^3} + 3{x^2} + ax + b\\\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {{x^4} - 3{x^3} + 4{x^2}} \right) - \left( {{x^2} - 3x + 4} \right) + ax - 3x + b + 4\\\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {{x^2} - 3x + 4} \right)\left( {{x^2} - 1} \right) + \left( {a - 3} \right)x + b + 4\\\,\,\,\,\,\,\,\,\,\,\,\,\, = {x^2}\left( {{x^2} - 3x + 4} \right) - \left( {{x^2} - 3x + 4} \right) + \left( {a - 3} \right)x + b + 4\\\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {{x^2} - 1} \right)f\left( x \right) + \left( {a - 3} \right)x + b + 4.\end{array}\)
Để \(f\left( x \right)\) chia hết cho \(g\left( x \right)\) thì \(\left\{ \begin{array}{l}a - 3 = 0\\b + 4 = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}a = 3\\b = - 4\end{array} \right..\)
Vậy \(a = 3,b = - 4\).
Chọn D.
