Mathematics

The key is recognizing that $h(x)$ is a product of two polynomials, so you can determine its properties by analyzing each factor separately. Notice that $x^2 - 1$ is even (symmetric about the $y$-axis) while $x^3 + 2x$ is odd (symmetric about the origin). When you multiply an even function by an odd function, the result is always odd—meaning $h(-x) = -h(x)$. This tells you something fundamental about the graph's symmetry and behavior.

The key is recognizing that $h(x)$ is a product of two polynomials, so you can determine its properties by analyzing each factor separately. Notice that $x^2 - 1$ is even (symmetric about the $y$-axis) while $x^3 + 2x$ is odd (symmetric about the origin). When you multiply an even function by an odd function, the result is always odd—meaning $h(-x) = -h(x)$. This tells you something fundamental about the graph's symmetry and behavior.