Pre Calc Checkup 3

Name:
Date:
Graded Assignment
Checkup: Solving Polynomial Equations

Answer the following questions using what you've learned from this lesson. Write your responses in the spaces provided, and turn the assignment in to your instructor.

List all possible rational zeros for each polynomial function.

1.

-3, 2, 5

2.

-12, 17. 27

Use Descartes' rule of signs to describe the roots for each polynomial function.

3.

Two sign changes = Two or no positive roots

m(-x) = (-x)3 + 3(-x)2 – 18(-x) – 40 = -x + 3x + 18x - 40

Two sign changes = Two or no positive roots
4.

Three sign changes = Three or one positive roots

w(-x) = (-x)4 + 4(-x)3 – 7(-x)2 + 20(-x) - 21 = x – 4x – 7x – 20x – 21

No sign changes = No negative roots
Find an upper bound and a lower bound for the zeros of the following polynomial functions.

5.

Upper Bound: 8
Lower Bound: -6

6.

Upper Bound: 3
Lower Bound: 2

Factor each polynomial completely over the set of complex numbers.

7.

8.

9.

Write a polynomial that has the given numbers as roots.

10.

11.

Use the graph to guess one zero for the polynomial whose graph is shown. Then factor completely.

12.

13.

14. Solve the quadratic equation by the method of square roots:
.

x = sqrt -1

Solve each equation over the set of complex numbers.

15.

16.