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

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

   Step (a):

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

   $8 − 24 + 14 + 2 = 0$

   Answer (a):

   $0 = 0$

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

   Hint (b):

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

   Answer (b):

   $\left(x − 2\right)$

3. Use (b) to find another factor.

   Step (c):

   Try using a generic rectangle.

   Answer (c):

   $\left(x^{2} − 4x −1\right)$

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

   Hint (d):

   See part (a) for one solution.

   Step (d):

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

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

   Answer (d):

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