Đáp án:
$\begin{array}{l}
8)\\
H = \left( { - 3x + 5} \right)\left( {x - 6} \right) - \left( {x - 1} \right)\left( {{x^2} - 2x + 3} \right)\\
+ \left( {x + 2} \right)\left( {{x^2} - 3} \right)\\
= - 3{x^2} + 18x + 5x - 30\\
- \left( {{x^3} - 2{x^2} + 3x - {x^2} + 2x - 3} \right)\\
+ {x^3} - 3x + 2{x^2} - 6\\
= - 3{x^2} + 23x - 30 - {x^3} + 3{x^2} - 5x + 3\\
+ {x^3} + 2{x^2} - 3x - 6\\
= 2{x^2} + 15x - 33\\
Khi:x = - 1\\
\Leftrightarrow H = 2.{\left( { - 1} \right)^2} + 15.\left( { - 1} \right) - 33\\
= - 46\\
9)L = 5x\left( {x - 1} \right)\left( {2x + 3} \right) - 10x\left( {{x^2} - 4x + 5} \right)\\
- \left( {x - 1} \right)\left( {x - 4} \right)\\
= 5x\left( {2{x^2} + x - 3} \right) - 10{x^3} + 40{x^2} - 50x\\
- {x^2} + 5x - 4\\
= 10{x^3} + 5{x^2} - 15x - 10{x^3} + 40{x^2} - 50x\\
- {x^2} + 5x - 4\\
= 44{x^2} - 60x - 4\\
Khi:x = - \dfrac{1}{3}\\
\Leftrightarrow L = 44.{\left( {\dfrac{{ - 1}}{3}} \right)^2} - 60.\dfrac{{ - 1}}{3} - 4\\
= \dfrac{{44}}{9} + 16\\
= \dfrac{{188}}{9}\\
10)M = - 7x\left( {x - 5} \right) - \left( {x - 1} \right)\left( {{x^2} - x - 2} \right)\\
+ {x^2}\left( {x - 3} \right) - 5x\left( {x - 8} \right)\\
= - 7{x^2} + 35x - \left( {{x^3} - {x^2} - 2x - {x^2} + x + 2} \right)\\
+ {x^3} - 3{x^2} - 5{x^2} + 40x\\
= - 7{x^2} + 35x - {x^3} + 2{x^2} + x - 2\\
+ {x^3} - 8{x^2} + 40x\\
= - 13{x^2} + 76x - 2\\
Khi:x = \dfrac{1}{2}\\
\Leftrightarrow M = - 13.\dfrac{1}{4} + 76.\dfrac{1}{2} - 2\\
= - \dfrac{{13}}{4} + 36\\
= \dfrac{{ - 13 + 144}}{4} = \dfrac{{ - 131}}{4}
\end{array}$
