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Self-Quiz: Finding Roots of Polynomials



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

 1. 

If mc001-1.jpg is a factor of mc001-2.jpg, then which of these statements is/are true?
           I.  mc001-3.jpg is a root of the polynomial.
           II.  mc001-4.jpg divides into mc001-5.jpg with no remainder.
           III.  mc001-6.jpg 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 mc002-1.jpg have?
a.
6
c.
2 or 1
b.
3
d.
Cannot be determined.
 

 3. 

List all of the possible rational roots of mc003-1.jpg.
a.
mc003-2.jpg
c.
mc003-4.jpg
b.
mc003-3.jpg
d.
mc003-5.jpg
 

 4. 

A student has found that x = -6 is a rational root of mc004-1.jpg.  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 mc004-2.jpg 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 mc005-1.jpg.  Locate the other two roots?
a.
mc005-4.jpg
c.
mc005-6.jpg
b.
mc005-5.jpg
d.
mc005-7.jpg
 

 6. 

Find all the roots of the polynomial, mc006-1.jpg.
a.
mc006-7.jpg
c.
mc006-9.jpg
b.
mc006-8.jpg
d.
mc006-10.jpg
 

 7. 

Using Descartes’ Rule of Signs, determine how many of the roots of the polynomial mc007-1.jpg will be positive real numbers, negative real numbers and imaginary numbers.
a.
2 positive real #
1 negative real #’s
0 imaginary #’s
c.
1 positive real #
0 negative real #’s
2 imaginary #’s
b.
1 positive real #
2 or 0 negative real #’s
2 or 0 imaginary #’s
d.
2 or 0 positive real #
2 or 0 negative real #’s
1 or 3 imaginary #’s
 



 
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