Rational Root Theorem Test – Precalculus Math (Printable PDF)

Question 1 Find All Zeros (2 points)

Find all zeros of P(x) = 2x³ + x² − 13x + 6.

Question 2 Conjugate Zeros and Intercepts (2 points)

Suppose Q has degree 4 and real coefficients, and two of its zeros are 1 + 3i and −2i.

1. Name the other two zeros. (1 point)
2. How many x-intercepts does its graph have? Explain. (1 point)

Question 3 Zeros and End Behavior from a Graph (2 points)

The graph shows a degree-3 polynomial that touches the x-axis at −4 and crosses it at 1.

1. Find the multiplicity of each zero. (1 point)
2. Describe the end behavior and write a possible equation. (1 point)

Question 4 Slant and Vertical Asymptotes (2 points)

Let f(x) = 4x² − 5x + 3x − 1. Find the slant asymptote and the vertical asymptote.

Question 5 Polynomial Inequality (2 points)

Solve 2x³ − x² − 15x ≤ 0.

Question 6 Rational Inequality (3 points)

Solve x + 4x − 1 < 3, giving the solution set as intervals.

Question 7 Build a Polynomial (2 points)

Write the monic polynomial of least degree with real coefficients that has a double zero at −1 and a zero at 3i. Expand to standard form.

Question 8 Analyze a Rational Function (3 points)

The graph of f(x) = x² + x − 6x − 1 is shown with its dashed asymptotes.

1. Write the equation of the vertical asymptote. (1 point)
2. Use division to find the slant asymptote. (1 point)
3. Find the x-intercepts. (1 point)

Question 9 Unit Cost Over Time (2 points)

A workshop’s average cost per item is A(n) = 5n + 1200n dollars for n items.

1. Find the horizontal asymptote and say what it means. (1 point)
2. How many items make the average cost at most $15? (1 point)