QuestionState the number of $x$-intercepts for the polynomial function: $$h(x)=2 x(x+3)(x-3)^{2}$$

Studdy Solution
Count the number of distinct $x$-intercepts by considering the roots of each factor:
- The factor $x$ gives an $x$-intercept at $x = 0$. - The factor $(x+3)$ gives an $x$-intercept at $x = -3$. - The factor $(x-3)^2$ gives an $x$-intercept at $x = 3$.
Since each factor contributes a distinct $x$-intercept, the total number of distinct $x$-intercepts is 3.
The number of $x$-intercepts is $\boxed{3}$.