### Home > A2C > Chapter Ch9 > Lesson 9.3.1 > Problem 9-121

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 appears to be an integer solution to the equation?

Check your answer from part (a) in the equation.

Since

*x*= −7 is a solution to the equation, what is the factor associated with this solution?Use polynomial division to find the other factor.

Use your new factor to complete this equation: Homework Help ✎

*x*^{3}+ 5*x*^{2}− 16*x*−14 = (*x*+ 7)(*other factor*)**=**0The “other factor” leads to two other solutions to the equation. Find these two new solutions and give all three solutions to the original equation.

*x* = −7

*y* = −343 + 245 + 112 −14*y* = 0

(*x* + 7)

Divide *x*^{3} + 5*x*^{2} −16*x* −14 by *x* + 7 using a generic rectangle.

*x*^{2} −2*x* −2

*x* ^{3} + 5*x* ^{2} − 16*x* − 14 = (*x* + 7)(*x* ^{2} − 2*x* − 2) = 0

Try using the quadratic formula.