High schoolers generate the equation of a polynomial given its roots and the end behavior of the function. They need to apply theorems concerning the multiplicity of roots, conjugates of irrational or imaginary roots to find a...

Here is a lesson that starts with having geometers translate points using compass directions into an accurate picture of the problem. Then they must use their knowledge of the Pythagorean theorem or similar triangles to solve. This makes...

An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving. 

Young scholars convert quadratic functions from standard form to vertex form. In this algebra instructional activity, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor...

Bring some concrete reasoning to the skills of multiplying and combining terms. Using various strategies, the six activities in the module provide practice for the skills of adding, subtracting, multiplying, and diving polynomials. The...

In this math learning exercise, students practice graphing functions and define the domain. Then they use Lagrange's Theorem to estimate the error involved in using the two Taylor polynomials.

In this dividing polynomials worksheet, high schoolers divide 42 polynomials.  Students factor polynomials using synthetic division and long division.

Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...

Students factor polynomials and use long division t solve problems. In this algebra lesson, students find the zeros of polynomials by synthetic and long division. They perform operation using complex numbers.

Students determine the monotonicity and concavity properties of a function, then apply the First Derivative Test and draw conclusions about the first and second derivatives from these properties.

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...

This tutorial contains a lesson about the remainder and factor theorems along with practice problems.

Provides examples and a video lesson that illustrate the remainder and factor theorems. [1:34]

The online assessment demonstrates knowledge of advanced mathematical concepts in Algebra II. The questions test students on the remainder and factor theorems.

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...

An introduction to two important uses of synthetic substitution, the remainder theorem and the factor theorem. Includes examples and sample problems with solutions.

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...

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.

Practice solving division problems with 0s in the solution, or quotient. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

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...

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.

Math Forum offers a description of remainder and factor theorem and gives and example of their uses.

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....

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.