Lawrence Hall of Science
The Math Page: Topics in Pre Calculus: Synthetic Division by X A
Here is a site that clearly and thoroughly explains how to divide a polynomial by a binomial using synthetic division. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point...
Purple Math
Purplemath: Factor Theorem
Purplemath.com discusses the Factor Theorem, explaining its relationship to the Remainder Theorem. The lesson has a link to synthetic division, a key to discovering if a value is a root.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes, Factorization of Quadratic Polynomial Ii
This task is intended to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions. The argument here generalizes to show that a polynomial of degree d can have at most d roots....
Illustrative Mathematics
Illustrative Mathematics: A Apr the Missing Coefficient
The purpose of this task is to emphasize the use of the Remainder Theorem as a method for determining structure in polynomials in equations, and in this particular instance, as a replacement for division of polynomials. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of a General Polynomial
In this task, students investigate the properties of a polynomial of degree d > 0. The task relates to the Fundamental Theorem of Algebra. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of Quadratic Polynomial
This is the first of a series of problems building to an understanding of an important property of polynomial functions, that a polynomial of degree d can have at most d roots. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A apr.b.3 and a apr.b.2: Graphing From Factors Iii
The task has students use the remainder theorem to deduce a linear factor of a cubic polynomial, and then to completely factor the polynomial. Aligns with A-APR.B.3 and A-APR.B.2.
Khan Academy
Khan Academy: Algebra Ii: Remainder Theorem
Use the PRT (Polynomial Remainder Theorem) to determine the factors of polynomials and their remainders when divided by linear expressions. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a...
Interactive Mathematics
Interactive Mathematics: The Remainder and the Factor Theorem
This tutorial contains a lesson about the remainder and factor theorems along with practice problems.
CK-12 Foundation
Ck 12: Algebra Ii: 11.12 Remainder Theorem
This lesson explores polynomial division with remainders, and the important relationship between a polynomial's remainders and its solutions.
Curated OER
Real Roots of Polynomial Functions
A thorough abstract treatment of how to find the roots of a polynomial function. The site explains how to divide polynomials and the remainder theorem. The language is a bit technical, but the examples are good.
Windstream
Ojk's Precalculus Study Page: Remainder and Factor Theorems
An introduction to two important uses of synthetic substitution, the remainder theorem and the factor theorem. Includes examples and sample problems with solutions.
Sophia Learning
Sophia: Evaluating Polynomials With the Remainder Theorem: Lesson 3
This lesson shows how the Remainder Theorem can be used to evaluate a polynomial for a given x value. It is 3 of 6 in the series titled "Evaluating Polynomials With The Remainder Theorem."
Sophia Learning
Sophia: Evaluating Polynomials With the Remainder Theorem: Lesson 4
This lesson shows how the Remainder Theorem can be used to evaluate a polynomial for a given x value. It is 4 of 6 in the series titled "Evaluating Polynomials With The Remainder Theorem."
Sophia Learning
Sophia: Evaluating Polynomials With the Remainder Theorem: Lesson 6
This lesson shows how the Remainder Theorem can be used to evaluate a polynomial for a given x value. It is 6 of 6 in the series titled "Evaluating Polynomials With The Remainder Theorem."
Sophia Learning
Sophia: Finding Roots With the Remainder Theorem: Lesson 3
This lesson uses the remainder theorem to determine whether a given value of x is a root of a given polynomial. It is 3 of 5 in the series titled "Finding Roots With The Remainder Theorem."
Interactive Mathematics
Interactive Mathematics: Polynomial Functions and Equations
Want to find the roots of a polynomial function? Learn how, using several methods in this tutorial. Graphing and Scientific Notebook are used on the main page. Click on the "Dinosaur Method" link at the bottom of the page to see the...
Purple Math
Purplemath: Remainder Theorem
Purplemath explains the Remainder Theorem and gives examples using synthetic division to evaluate, determine if a value is a solution/zero. The lesson contains a link to synthetic division and other related terms.