Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.46

Pre CAL.46 Use the Rational Root Theorem to List Possible Rational Zeros Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.46 Use the Rational Root Theorem to List Possible Rational Zeros. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.46 Use the Rational Root Theorem to List Possible Rational Zeros - Use the Rational Root Theorem to List Possible Rational Zeros

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.46 Use the Rational Root Theorem to List Possible Rational Zeros skill assessments:

Problem 1Difficulty: Mastery

How many rational zeros does P(x) actually have? P(x) = −24x⁵ − 23x⁴ + 115x³ + 219x² + 218x + 80

Solution & Explanation:Use the Rational Root Theorem to list candidates, then test them. The rational zeros are {-2, -5/8, 8/3}, so there are 3 rational zeros.

Problem 2Difficulty: Mastery

How many possible rational zeros does P(x) have according to the Rational Root Theorem? P(x) = −8x⁵ + 58x⁴ − 173x³ + 264x² − 204x + 63

Solution & Explanation:List factors of the constant term 63 (p values) and factors of the leading coefficient -8 (q values). Form all reduced ±p/q values and remove duplicates. The number of candidates is 48.

Problem 3Difficulty: Mastery

After listing candidates with the Rational Root Theorem, test to find the rational zeros. Which set lists all rational zeros of P(x)? P(x) = −12x⁵ − 68x⁴ − 95x³ − 80x² − 83x − 12

A{-4, -3/2}

B{-4, -3/2, -1/6, 1/2}

C{-4, -3/2, 1/6}

D{-4, -3/2, -1/6}

Solution & Explanation:First list possible rational zeros ±(p/q) using factors of -12 and -12. Then test each candidate. The candidates that make P(x)=0 are the rational zeros, which are {-4, -3/2, -1/6}.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.46 (Use the Rational Root Theorem to List Possible Rational Zeros).