Students factor higher-degree real-coefficient polynomials using common factors, grouping, identities, substitution, the Rational Root Theorem, the Factor Theorem, and polynomial division, and solve equations for real and nonreal complex roots, including repeated roots and multiplicities. They perform long division and synthetic division by linear divisors, using placeholders for missing powers, and apply the Remainder Theorem to evaluate polynomials and connect remainders, factors, and zeros. They determine rational-function restrictions, holes, vertical, horizontal, and slant asymptotes, solve rational equations and inequalities through domain and sign analysis, and sketch polynomial functions using zeros, multiplicities, degree, leading coefficient, intercepts, and end behavior.
On this page:
- Master skills like “Use the factor theorem”, “Use the remainder theorem”, and “Solve polynomial equations” with unlimited, free practice problems
- Download (or modify) free worksheets on Polynomial and Rational Functions you can use at home or in class with practice problems across all skills in this group including “Factor higher-degree polynomials”, “Solve rational equations and inequalities”, “Divide polynomials using synthetic division”.
- Start working on adaptive units like “Polynomials Factoring - Factor Theorem and Synthetic Division - Intro” or “Polynomials Factoring - Factor Theorem and Synthetic Division - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Polynomial and Rational Functions: Individual Skills
Master 7 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
Practice 'Determine restrictions of rational functions'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
Hover a skill above to start practicing.
Download/Modify Free Grade 12 'Polynomial and Rational Functions' Worksheet
Print this free 'Polynomial and Rational Functions' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Determine restrictions of rational functions
- Divide polynomials using synthetic division
- Factor higher-degree polynomials
- Solve polynomial equations
- Solve rational equations and inequalities
- Use the factor theorem
- Use the remainder theorem
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Polynomial and Rational Functions) through scaffolded problems that grow in difficulty as concepts are understood.