$\begin{array}{l} A = \left\{ {x \in R|{x^4} - 3{x^2} - 4 \le 0} \right\}\\ {x^4} - 3{x^2} - 4 = \left( {{x^2} + 1} \right)\left( {{x^2} - 4} \right) \le 0\\ \Leftrightarrow {x^2} - 4 \le 0 \Leftrightarrow {x^2} \le 4 \Leftrightarrow - 2 \le x \le 2\\ \Rightarrow A = \left[ { - 2;2} \right]\\ B = \left\{ {x \in R|{x^3} + 2{x^2} + 3x > 0} \right\}\\ {x^3} + 2{x^2} + 3x > 0 \Leftrightarrow x\left( {\underbrace {{x^2} + 2x + 3}_{ > 0}} \right) > 0\\ \Leftrightarrow x > 0 \Rightarrow B = \left( {0; + \infty } \right)\\ A \cup B = \left[ { - 2; + \infty } \right)\\ A \cap B = \left( {0;2} \right]\\ A\backslash B = \left[ { - 2;0} \right]\\ {C_R}B =(-\infty;0] \end{array}$
