CPM Homework Help : A2C Problem 9-149

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?

Step (a):

Substitute 2 into the equation for every x.

8 − 24 + 14 + 2 = 0

Answer (a):

0 = 0

Hint (b):

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

Answer (b):

(x − 2)

Step (c):

Try using a generic rectangle.

Answer (c):

(x² − 4x −1)

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):

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