Carlos is always playing games with his graphing calculator, but now his calculator has contracted a virus. The
, , and functions on his calculator are not working. He needs to solve x3 + 5x2 – 16x – 14 = 0, so he graphs y = x3 + 5x2 – 16x – 14 and sees the graph below in the standard window. Homework Help ✎
From the graph, what number appears to be an integer solution to the equation?
Verify that your answer to part (a) is a solution.
Since you know a solution to the equation, what is the factor associated with this solution?
Use polynomial division to determine the other factor.
Use your new factor to complete the following equation.
x3 + 5x2 – 16x – 14 = 0
(x + 7)(other factor) = 0
The “other factor” leads to two other solutions to the equation. What are the two other solutions? State all three solutions to the original equation.
x = −7
Substitute your answer from part (a) into the original equation.
(x + 7)
Divide x3 + 5x2 − 16x − 14 by (x + 7) using an area model.
x2 − 2x − 2
(x + 7)(x2 − 2x − 2) = 0
Use the Quadratic Formula on the "other factor".