Đáp án:
$\begin{array}{l}
a){x^3} - {x^2} + 11x + 16\\
= {x^3} - 3x - {x^2} + 3 + 14x + 13\\
= x\left( {{x^2} - 3} \right) - \left( {{x^2} - 3} \right) + 14x + 13\\
= \left( {{x^2} - 3} \right)\left( {x - 1} \right) + 14x + 13\\
\Rightarrow \left( {{x^3} - {x^2} + 11x + 16} \right):\left( {{x^2} - 3} \right)\\
= x - 1\,\text{dư}\,14x + 13\\
\Rightarrow 14x + 13 = 4\\
\Rightarrow x = - \frac{9}{{14}}\\
\text{Vậy}\,x = - \frac{9}{{14}}\\
b)\left( {{x^3} + 6{x^2} - 15} \right)\\
= {x^3} + 2x + 6{x^2} + 12 - 2x - 27\\
= x\left( {{x^2} + 2} \right) + 6\left( {{x^2} + 2} \right) - 2x - 27\\
= \left( {{x^2} + 2} \right)\left( {x + 6} \right) - 2x - 27\\
\Rightarrow \left( {{x^2} + 2} \right)\left( {x + 6} \right):\left( {{x^2} + 2} \right)\\
= x + 6\,\text{dư}\, - 2x - 27\\
\Rightarrow - 2x - 27 = 5\\
\Rightarrow 2x = - 32\\
\Rightarrow x = - 16\\
\text{Vậy}\,x = - 16
\end{array}$
