10
lesson pretestMultiple Choice

Pretest

Question 10 • Math 3

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 15 x to the 11th power minus 6 x to the 8th power plus x cubed minus 4 x plus 3 ?

Answer
A
plus or minus 1 over 15 , plus or minus 1 fifth , plus or minus 1 third , plus or minus 3 fifths , plus or minus 1 , plus or minus 3
B
plus or minus 1 third , plus or minus 1 , plus or minus 3
C
plus or minus 1 third , plus or minus 1 , plus or minus 5 thirds , plus or minus 3 , plus or minus 5 , plus or minus 15
D
plus or minus 1 over 15 , plus or minus 1 fifth , plus or minus 1 third , plus or minus 3 fifths , plus or minus 1 , plus or minus 5 thirds , plus or minus 3 , plus or minus 5 , plus or minus 15

Explanation

The Rational Root Theorem says any potential rational root is a factor of the constant term divided by a factor of the leading coefficient. Here, the constant term is 3 and the leading coefficient is 15, so the candidates come from ±1 or ±3 over 1, 3, 5, or 15. After reducing duplicates, these are ±1/15, ±1/5, ±1/3, ±3/5, ±1, and ±3, which matches choice A.

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