Name:    Self-Quiz: Finding Roots of Polynomials

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

If is a factor of , then which of these statements is/are true?
I.  is a root of the polynomial.
II.  divides into with no remainder.
III.  is an x-intercept on the graph of the polynomial.
 a. I only c. II only b. I and II only d. I, II and III

2.

How many roots does the polynomial have?
 a. 6 c. 2 or 1 b. 3 d. Cannot be determined.

3.

List all of the possible rational roots of .
 a. c. b. d.

4.

A student has found that x = -6 is a rational root of .  How could the student locate the other two roots?
 a. Factor the polynomial by grouping terms. c. Factor x out of the first three terms of the polynomial, then factor the remaining quadratic.  Set each factor equal to zero and solve. b. Keep doing synthetic division with new divisors until you get two more numbers with remainder zero. d. Divide into the polynomial (synthetically); solve the equation with the resulting quotient (now a degree two polynomial) set equal to zero.

5.

A student has found that x = -6 is a rational root of .  Locate the other two roots?
 a. c. b. d.

6.

Find all the roots of the polynomial, .
 a. c. b. d.

7.

Using Descartes’ Rule of Signs, determine how many of the roots of the polynomial will be positive real numbers, negative real numbers and imaginary numbers.
 a. 2 positive real #1 negative real #’s0 imaginary #’s c. 1 positive real #0 negative real #’s2 imaginary #’s b. 1 positive real #2 or 0 negative real #’s2 or 0 imaginary #’s d. 2 or 0 positive real #2 or 0 negative real #’s1 or 3 imaginary #’s