### Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem8-112

8-112.
1. 8-112. Carlo is trying to factor the polynomial p(x) = x4 – 4x3 – 4x2 + 24x – 9 to determine all of its zeros. He discovers one factor by making a guess and dividing the polynomial, so he has p(x) = (x – 3)(x3x2 – 7x + 3). Now he is trying to factor x3x2 – 7x + 3, so he tries dividing it by (x + 3), then by (x + 1), and finally by (x – 1), but none works without a remainder. Then Teo comes by and says, “You should look at the graph.” Homework Help ✎

1. How does the graph help?

2. Complete the problem.

It shows that x = 3 is a double root, so (x − 3) is a repeated factor.

Divide x3x2 − 7x + 3 by (x − 3).

Now use the Quadratic Formula to solve for x.

$x = 3, -1 \pm \sqrt{2}$