3
practice testMultiple Choice

Practice Test

Question 3 • Advanced Algebra: Concepts and Connections

The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

Answer
A
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
B
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
C
plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
D
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3

Explanation

Factor out x: f(x) = x(3x⁴ − 2x + 7), so 0 is one potential root. For the remaining polynomial, the Rational Root Theorem says candidates are factors of 7 divided by factors of 3: ±1, ±7, ±1/3, and ±7/3. Together with 0, these match choice A.

AI-written and checked against the verified answer.

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