Benjamin Franklin High School
Saxon Math: Algebra 2 (Section 4)
This fourth of twelve units in a series continues the investigation of functions through equations and inequalities. However, the modular nature of the lessons in the section make this an excellent resource for any curriculum...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
Mathematics Assessment Project
Representing Polynomials
Use this complete and very detailed lesson plan to assess your students' understanding of two important behaviors of polynomials. The first is the relationship between the zeros of a polynomial function and the function's graph, and the...
Curated OER
Watch Your P's and Q's
Using your graphing calculator, find all the rational zeroes of a polynomials by using the Rational Zero Theorem. Divide polynomials using the Remainder Theorem and the Factor Theorem and then graph it to find the number of real roots.
Illustrative Mathematics
The Missing Coefficient
This activity highlights the use of the remainder theorem to solve for the unknown coefficient of a specified polynomial when given one of its factors. Use this single problem as a warm-up exercise, a quick check-in at the end of a...
Illustrative Mathematics
Zeroes and Factorization of a General Polynomial
These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...
Illustrative Mathematics
Zeroes and factorization of a non polynomial function
Functions behaving badly: the squaring function and the absolute value function are both zero at x=0. Yet when you divide each by x, different things happen. Here, your class will explore each scenario as a means to adding depth to their...
Illustrative Mathematics
Zeroes and factorization of a quadratic polynomial I
This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...
Curated OER
Multiplicity of Zeros of Functions
Pupils identify the multiplicity of exponents as they graph polynomials. They write equations for a function given the zeros of the function and work backwards from solving equations.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Polynomial and Rational Functions
Hotmath provides 20 practice problems that relate to polynomial and rational functions. Each of the practice problems include a step-by-step guide for solving.
Varsity Tutors
Varsity Tutors: Hotmath: Polynomial Division: The Remainder and Factor Theorems
Thirty-nine problems present a variety of practice applying the remainder and factor theorems to polynomial division.
Paul Dawkins
Paul's Online Notes: Algebra: Finding Zeroes of Polynomials
This tutorial looks at a process using the Rational Root Theorem that allows you to find some of the zeroes of a polynomial and in special cases all of the zeroes.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Long Division of Polynomials
Question and Answer session on long division of polynomials involving remainders. See how this problem was solved.
Washington State University
Washington State University: Polynomial Division
This site contains a brief explanation of how to divide a polynomial by a monomial by factoring.
Richland Community College
Real Zeros of Polynomial Functions
This site from the Richland Community College contains information on long and synthetic division, the remainder theorem and the factor theorem.
Texas Instruments
Texas Instruments: Polynomials
These questions about polynomials involve finding the zeros, writing the equation of the polynomial given the zeros, and determining the end behavior. Questions are multiple choice and true/false; solutions are provided.
Texas Instruments
Texas Instruments: The Remainder Theorem, Polynomial Expansion, and Tangent Line
In this Derive activity, students use the Remainder Theorem to find a tangent line to the graph of a polynomial function.
Texas A&M University
Wtamu Virtual Math Lab: College Algebra: Long Division
You will learn how to divide one polynomial by another using long division by viewing example problems and step-by-step solutions and completing practice questions.
Texas A&M University
Wtamu Virtual Math Lab: College Algebra: Synthetic Division
This tutorial will show you how to use synthetic division and how to use both the remainder and factor theorems in conjunction with synthetic division. Offers several examples with solutions and explanations as well as practice problems...
Texas A&M University
Wtamu Virtual Math Lab: College Algebra: Rational Zero Theorem
This tutorial will show you how to use the rational zero theorem, to find all zeros of a polynomial function, and how to use Descartes' rule of signs. Offers step-by-step solutions to example problems as well as practice problems for you...
Math Medics
S.o.s. Math: Polynomial Long Division
This tutorial offers a description and examples of long division using polynomials. Exercises with answers also provided.
Other
Math Help Algebra Synthetic Division
Works through a step-by-step example that gives a good explanation of how to do synthetic division. Also provides other example problems.
Math Planet
Math Planet: Algebra 2: Polynomial Functions: Remainder and Factor Theorems
Provides examples and a video lesson that illustrate the remainder and factor theorems. [1:34]
McGraw Hill
Glencoe Mathematics: Quiz on the Remainder and Factor Theorems
The online assessment demonstrates knowledge of advanced mathematical concepts in Algebra II. The questions test students on the remainder and factor theorems.