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

9-149.
1. Given the equation x3 − 6x2 + 7x + 2 = 0. Homework Help ✎

1. Verify that x = 2 is a solution.

2. What is one factor of x3 − 6x2 + 7x + 2?

3. Use (b) to find another factor.

4. What are all the solutions of x3 − 6x2 + 7x + 2 = 0?

Substitute 2 into the equation for every x.

8 − 24 + 14 + 2 = 0

0 = 0

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

(x − 2)

Try using a generic rectangle.

(x2 − 4x −1)

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.

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