\[\boxed{\text{390\ (390).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left( x^{2} + 17 \right)(x - 6)(x + 2) < 0\]
\[x^{2} + 17 > 0\ при\ любом\ x\]
\[\Longrightarrow (x + 2)(x - 6) < 0\]
\[x \in ( - 2;6).\]
\[\textbf{б)}\ \left( 2x^{2} + 1 \right) \cdot x \cdot (x - 4) > 0\]
\[так\ как\ 2x^{2} + 1 > 0\]
\[\Longrightarrow x(x - 4) > 0\]
\[x \in ( - \infty;0) \cup (4; + \infty).\]
\[\textbf{в)}\ (x - 1)^{2}(x - 24) < 0\]
\[(x - 1)^{2} \geq 0\ при\ любом\ \]
\[значении\ x;\]
\[x - 24 < 0;\ \ \ x \neq 1.\]
\[x \in ( - \infty;1) \cup (1;24).\]
\[\textbf{г)}\ (x + 7)(x - 4)^{2}(x - 21) > 0\]
\[(x - 4)^{2} \geq 0\ при\ любом\ x;\]
\[(x + 7)(x - 21) > 0;\ \ \ \ x \neq 4.\]
\[x \in ( - \infty; - 7) \cup (21; + \infty).\]