Đáp án:
$\begin{array}{l}
{x^3} + 2x + {x^2}\\
= x.\left( {{x^2} + 2 + x} \right)\\
= x.\left( {{x^2} + x + 2} \right)\\
a){x^2}\left( {{x^2} + 1} \right) - {x^2} - 1\\
= {x^2}\left( {{x^2} + 1} \right) - \left( {{x^2} + 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {{x^2} - 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {x + 1} \right)\left( {x - 1} \right)\\
Khi:{x^2}\left( {{x^2} + 1} \right) - {x^2} - 1 = 0\\
\Leftrightarrow \left( {{x^2} + 1} \right)\left( {x + 1} \right)\left( {x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right.\\
Vay\,x = 1;x = - 1\\
b)5x{\left( {x - 3} \right)^2} - 5{\left( {x - 1} \right)^3} + 15\left( {x + 2} \right)\left( {x - 2} \right)\\
= 5x\left( {{x^2} - 6x + 9} \right) - 5\left( {{x^3} - 3{x^2} + 3x - 1} \right)\\
+ 15\left( {{x^2} - 4} \right)\\
= 5{x^3} - 30{x^2} + 45x - 5{x^3} + 15{x^2} - 15x + 5\\
+ 15{x^2} - 60\\
= 30x - 55\\
Khi:30x - 55 = 5\\
\Leftrightarrow 30x = 60\\
\Leftrightarrow x = 2\\
Vay\,x = 2
\end{array}$
