### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-149

9-149.

Given the equation $x^{3} − 6x^{2} + 7x + 2 = 0$.

1. Verify that $x = 2$ is a solution.

Substitute $2$ into the equation for every $x$.

$8 − 24 + 14 + 2 = 0$

$0 = 0$

2. What is one factor of $x^{3} − 6x^{2} + 7x + 2$?

Use the value for x given in problem a to calculate the factor.

$\left(x − 2\right)$

3. Use (b) to find another factor.

Try using a generic rectangle.

$\left(x^{2} − 4x −1\right)$

4. What are all the solutions of $x^{3} − 6x^{2} + 7x + 2 = 0$?

See part (a) for one solution.

$\frac{4\pm\sqrt{16+4}}{2}$

Use the quadratic formula to find the other solutions in the equation x2 − 4x − 1.

$x=2, 2\pm\sqrt{5}$