1. **State the problem:** Find a cubic polynomial function $f(x)$ with zeros at $-2$, $3$, and $5$, and that passes through the point $(7,144)$. 2. **Write the general form:** Since the zeros are $-2$, $3$, and $5$, the polynomial can be written in factored form as: $$f(x) = a(x + 2)(x - 3)(x - 5)$$ where $a$ is a constant to be determined. 3. **Use the given point to find $a$:** Substitute $x=7$ and $f(7)=144$ into the equation: $$144 = a(7 + 2)(7 - 3)(7 - 5)$$ Calculate the factors: $$144 = a(9)(4)(2)$$ $$144 = a \times 72$$ 4. **Solve for $a$:** $$a = \frac{144}{72}$$ $$a = 2$$ 5. **Write the final polynomial:** $$f(x) = 2(x + 2)(x - 3)(x - 5)$$ This is the cubic polynomial in factored form that satisfies the given conditions.