Carlo was trying to factor the polynomial p(x) = x4 − 4x3 − 4x2 + 24x − 9 and find all of its roots. He had already found one factor by making a guess and trying it, so he had p(x) = (x − 3)(x3 − x2 − 7x + 3). He was trying to factor x3 − x2 − 7x + 3, and he had tried (x + 3), (x + 1), and (x − 1), but none worked. Then Teo came by and said, “You should look at the graph.” Homework Help ✎
How does the graph help?
Complete the problem.
It shows us that 3 is a double root which means (x − 3)2 is a factor.
Divide x3 − x2 − 7x + 3 by x − 3.
Use a multiplication rectangle to set it up.
Now use the quadratic formula to solve for x.