Algebra-2

Question Analysis
This question requires students to solve a cubic equation by factoring in a real-world context. It tests their ability to apply the zero product property and factor polynomials to find the values of for which the profit is zero.

Key Concept Explanation
The key concept here is the application of the zero product property to find the roots of the polynomial, which represent the values of for which the profit is zero.

Step-by-step Solution
1. Use the Rational Root Theorem to list possible rational roots:
2. Test : , so is a root.
3. Divide the polynomial by using synthetic division or polynomial long division to get: