### Home > CCA2 > Chapter 8 > Lesson 8.3.1 > Problem8-120

8-120.

Carlos is always playing games with his graphing calculator, but now his calculator has contracted a virus. The $\boxed{\text{TRACE}}$, $\boxed{\text{ZOOM}}$, and $\boxed{\text{WINDOW}}$ functions on his calculator are not working. He needs to solve
$x^3 + 5x^2 - 16x - 14 = 0$, so he graphs $y = x^3 + 5x^2 - 16x - 14$  and sees the graph at right in the standard window.

1.  From the graph, what appears to be an integer solution to the equation?

$x = -7$

2. Check your answers from part (a) in the equation.

Substitute your answer from part (a) into the original equation.

3. Since $x=-7$ is a solution to the question, what is the factor associated with this solution?

$(x + 7)$

4. Use polynomial division to find the other factor.

Divide $x^³ + 5x^² − 16x − 14$ by $x + 7$
using a generic rectangle. 2 by 3 rectangle, labeled as follows: left edge, x, & 7, top edge left, x squared, interior top left, x cubed.

Labels added to the rectangle, interior top middle, negative 2, x squared, interior bottom left, 7, x squared.

Labels added to rectangle, top edge, middle, negative 2, x, interior, bottom middle, negative 14, x, interior top left, negative 2, x.

Labels added to rectangle, top edge, right, negative 2, interior bottom right, negative 14.

$x^2 - 2x - 2$

1. Use your new factor to complete this equation:
$x^3 + 5x^2 - 16x - 14 =$($x+7$)(other factor)$=0$

2. The “other factor” leads to two other solutions to the equation. Find these two new solutions and give all three solutions to the original equation.

Use the Quadratic Formula with the answer found in part (d) that you used for part (e).