Set $x$ to $0$ and solve for y to find the y-intercept(s).
Set $y$ to $0$ and solve for x to find the x-intercept(s).

Let $x = 0$ to find the y-intercept.

$y = 2\left(0\right)³ − 10\left(0\right)² − \left(0\right)$

$0 = 2x³ − 10x² − x$
$0 = x\left(2x² − 10x² − 1\right)$

Let y = 0 to find the x-intercept. Then factor and use the Zero Product Property and the Quadratic Formula.

y-intercept: $\left(0,0\right)$

$x\text{-intercepts: } (0, 0)\text{ and }\left(\frac{5\pm3\sqrt{3}}{2},0\right)$

See part (a).

x-intercept: $\left(10, 0\right)$
no y-intercept