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Algebra 2 · Chapter 3 · Lesson 3.9 · Printable PDF

The Rational Root Theorem Worksheet with Answer Key

6 problems on the rational root theorem: listing every candidate root, finding all roots and linear factors, intersecting a curve and a line, clearing decimals first, a student's incomplete search, and proving a sum of square roots is a root of a quartic. 1 page, with a worked answer key.

6 problems1 pagesanswer key
Printable The rational root theorem worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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Try one first: a free Chapter 1 worksheet (PDF, no sign-in).

The full Algebra 2 courseEvery lesson in teaching order, with over 490 printables.See the course ›

What's on the worksheet

  1. List every candidate the theorem gives for each polynomial and count them.
    x^3 - 2x^2 + 5x + 106x^3 - x + 4-2x^3 + 6x - 15
  2. Find every root of a cubic and write it as a product of linear factors.
  3. Find the exact x-coordinates where a cubic curve meets a line.
  4. Explain why the theorem needs integer coefficients, rewrite the equation and solve it.
  5. Check Yuna's conclusion after testing all eight candidates.
  6. Show a number made from two square roots is a root of a quartic, then use the theorem on it.

Teach it first

The free lesson teaches it with worked examples and practice problems.

The rational root theorem: the lesson ›

More Chapter 3 worksheets: Polynomial functions