Đáp án:
$\begin{array}{l}
5.1\\
P\left( x \right) + Q\left( x \right)\\
= 3{x^2} + x - 4 + \left( { - 5{x^2}} \right) + x + 3\\
= \left( {3{x^2} - 5{x^2}} \right) + \left( {x + x} \right) + \left( { - 4 + 3} \right)\\
= - 2{x^2} + 2x - 1\\
P\left( x \right) - Q\left( x \right)\\
= 3{x^2} + x - 4 - \left( { - 5{x^2} + x + 3} \right)\\
= \left( {3{x^2} + 5{x^2}} \right) + \left( {x - x} \right) + \left( { - 4 - 3} \right)\\
= 8{x^2} - 7\\
5.2\\
A\left( x \right) + B\left( x \right)\\
= {x^3} - mx + {m^2} + \left( {m + 1} \right){x^2} + 3mx + {m^2}\\
= {x^3} + \left( {m + 1} \right){x^2} + 2mx + 2{m^2}\\
\Rightarrow Tổng\,hệ\,số:\\
1 + \left( {m + 1} \right) + 2m + 2{m^2}\\
= 2{m^2} + 3m + 2
\end{array}$
