### Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem8-121

8-121.
1. Given the polynomial p(x) = x3 – 6x2 + 7x + 2: Homework Help ✎

1. Use the Remainder Theorem to determine p(2).

2. Now use the Factor Theorem to determine one factor of x3 – 6x2 + 7x + 2. (See the Math Notes box in this lesson.)

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

Divide the polynomial by (x − 2). What is the remainder?

Since p(2) = 0, x = 2 is the zero of the function. What is the corresponding factor?

(x − 2)

Try using an area model.

(x2 − 4x − 1)

See part (a) for one solution.

Use the Quadratic Formula to find the solutions to
0 = x2 − 4x − 1.

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

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