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Rational Root Theorem Quiz – Precalculus (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Precalculus Math Quizzes – Mathbot, the Math Made Easy robot coach, with free printable quizzes for Precalculus
Looking for a rational root theorem quiz? Then this Precalculus quiz on Polynomial and Rational Functions: Zeros and Asymptotes asks 10 multiple-choice questions with instant feedback. Ten multiple-choice questions check zeros, end behavior, asymptotes and inequalities. Each wrong option reflects a real mistake, such as flipping p and q or including a zero of the denominator.

Standards: A-APR.B.2, A-APR.B.3, F-IF.C.7c, F-IF.C.7d, N-CN.C.9 · Level: Grade 12 Precalculus

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What this Polynomial and Rational Functions: Zeros and Asymptotes quiz checks

  • Rational candidates are p/q: p divides the constant term, q divides the leading coefficient.
  • A real-coefficient polynomial has non-real zeros in conjugate pairs.
  • The leading term decides end behavior: even or odd degree, positive or negative coefficient.
  • A slant asymptote appears when the numerator's degree is one more than the denominator's.
  • In a sign chart, zeros of the denominator are never included in the solution.

The 10 questions of the quiz

  1. Which number is NOT a possible rational zero of 2x3 + 5x2 − 4x − 3?
  2. Counting multiplicity, how many complex zeros does a polynomial of degree 7 have?
  3. A polynomial with real coefficients has the zero 4 − 3i. Which must also be a zero?
  4. What is the end behavior of f(x) = −3x4 + x2?
  5. The dashed slant line passes through (−1, −5) and (2, 4). Which equation describes it?
  6. The sign chart shows the sign of R(x), with zeros at −4, 2 and 6. Solve R(x) ≥ 0.
  7. Solve (x − 5)(x + 1) < 0.
  8. Solve x + 2x − 4 ≥ 0.
  9. What is the slant asymptote of x2 − 5x + 7x + 3?
  10. What is the horizontal asymptote of 6x2 + 12x2 − 9?

After the quiz

Missed a question? Reread the Polynomial and Rational Functions: Zeros and Asymptotes lesson, then take the quiz again. Next, solve the Precalculus worksheet on Polynomial and Rational Functions: Zeros and Asymptotes, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.

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