Revision history [back]

VOLUME A small box measures (x – 2) cm by x cm by (x + 8) cm. The volume of the box is 96 cm 2. Follow the steps below to find the dimensions of the box. (x + 8) cm (x – 2) cm x cm 1. Write an equation to model this situation. 2. One side of your equation is probably written in factored form. Explain why this does not help you solve the equation. 3. Rewrite the equation in standard form. Your equation should be in the form ax3 + bx2 + cx + d = 0. 4. Factory ax3 + bx2, where a and b are the coefficients from your equation. 5. Factor cx + d, where c and d are the coefficients from your equation. 6. Compare your answers in Exercises 4 and 5. What similarity do you notice? 7. Use your answers to Exercises 4-6 to rewrite the equation from Exercise 3 in factored form and then solve the equation. What are the three solutions? 8. Of the three solutions you wrote, which one makes sense in the context of the box problem? 9. What are the dimensions of the box?

VOLUME A small box measures (x – 2) cm by x cm by (x + 8) cm. The volume of the box is 96 cm 2. Follow the steps below to find the dimensions of the box. (x + 8) cm (x – 2) cm x cm 1. Write an equation to model this situation. 2. One side of your equation is probably written in factored form. Explain why this does not help you solve the equation. 3. Rewrite the equation in standard form. Your equation should be in the form ax3 + bx2 + cx + d = 0. 4. Factory ax3 + bx2, where a and b are the coefficients from your equation. 5. Factor cx + d, where c and d are the coefficients from your equation. 6. Compare your answers in Exercises 4 and 5. What similarity do you notice? 7. Use your answers to Exercises 4-6 to rewrite the equation from Exercise 3 in factored form and then solve the equation. What are the three solutions? 8. Of the three solutions you wrote, which one makes sense in the context of the box problem? 9. What are the dimensions of the box?