\begin{array}{l} \,\,\,\,2{x^4} + {x^3} - 5{x^2} - 3x - 3\\ = 2{x^4} - 6{x^2} + {x^3} - 3x + {x^2} - 3\\ = 2{x^2}\left( {{x^2} - 3} \right) + x\left( {{x^2} - 3} \right) + \left( {{x^2} - 3} \right)\\ = \left( {{x^2} - 3} \right)\left( {2{x^2} + x + 1} \right)\\ \Rightarrow \left( {2{x^4} + {x^3} - 5{x^2} - 3x - 3} \right):\left( {{x^2} - 3} \right)\\ \,\, = \left( {{x^2} - 3} \right)\left( {2{x^2} + x + 1} \right):\left( {{x^2} - 3} \right)\\ \,\, = 2{x^2} + x + 1 \end{array}
