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

8-112.

**8-112.**Carlo is trying to factor the polynomial*p*(*x*) =*x*^{4}– 4*x*^{3}– 4*x*^{2}+ 24*x*– 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)(*x*^{3}–*x*^{2}– 7*x*+ 3). Now he is trying to factor*x*^{3}–*x*^{2}– 7*x*+ 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 ✎How does the graph help?

Complete the problem.

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

Divide *x*^{3} − *x*^{2} − 7*x* + 3 by (*x* − 3).

Now use the Quadratic Formula to solve for *x*.