Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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 |
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2.
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How many roots does the polynomial  have? a. | 6 | c. | 2 or 1 | b. | 3 | d. | Cannot be
determined. |
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3.
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List all of the possible rational roots of  .
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4.
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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. |
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5.
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A student has found that x = -6 is a rational root of  .
Locate the other two roots?
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6.
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Find all the roots of the polynomial,  .
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7.
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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 #’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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