Giải thích các bước giải:
\[\begin{array}{l}
P(x) = {x^3} + a{x^2} + bx - 4\\
Q(x) = {x^2} - 4x + 3\\
P(x)\;chia\;Q(x)\;du\;(2x - 1)\\
\Rightarrow P(x) - (2x - 1) = (cx + d)Q(x) = (cx + d)({x^2} - 4x + 3) = c{x^3} + (d - 4c){x^2} + (3c - 4d)x + 3d\\
\Rightarrow {x^3} + a{x^2} + bx - 4 = c{x^3} + (d - 4c){x^2} + (3c - 4d + 2)x + 3d - 1\\
\left\{ \begin{array}{l}
c = 1\\
a = d - 4c\\
b = 3c - 4d + 2\\
3d - 1 = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = - 5\\
b = 9\\
c = 1\\
d = - 1
\end{array} \right.\\
Vay\;a = - 5;b = 9
\end{array}\]
