The equivalent factored expression you should have created in Try This 2 is −1(x − 7)(x + 1)(x − 4)(x − 2).

Substituting this into the equation at the beginning of the Explore section results in the following equation that can be used to determine when the whooping crane population is 45:

−1(x − 7)(x + 1)(x − 4)(x − 2) = 0

Try This 3

Use your knowledge of the zero-product property to solve the equation −1(x − 7)(x + 1)(x − 4)(x − 2) = 0.

1. Using the idea of the zero-product property, what should each factor of the polynomial equation −1(x − 7)(x + 1)(x − 4)(x − 2) = 0 equal?
2. Solve for x in the equation −1(x − 7)(x + 1)(x − 4)(x − 2) = 0.
3. Which solutions for x are reasonable answers to the question involving the population of whooping cranes over time?

Save your responses in your course folder.