### Home > INT3 > Chapter 8 > Lesson 8.3.1 > Problem 8-92

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 *x*^{3}+ 5*x*^{2}– 16*x*– 14 = 0, so he graphs*y*=*x*^{3}+ 5*x*^{2}– 16*x*– 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.

*x*^{3}+ 5*x*^{2}– 16*x*– 14 = 0

(*x*+ 7)(other factor) = 0The “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 *x*^{3} + 5*x*^{2} − 16*x* − 14 by (*x* + 7) using an area model.

*x*^{2} − 2*x* − 2

(*x* + 7)(*x*^{2} − 2*x* − 2) = 0

Use the Quadratic Formula on the "other factor".