In this lesson, students rewrite simple rational expressions in different forms, including representing remainders when dividing.
Students know and apply the Remainder Theorem and understand the role zeros play in the theorem.
The purpose of this task is to reinforce students’ prior knowledge of factoring and to introduce polynomial long division. The task draws connections between polynomial long division and division of whole numbers to support students in understanding the procedure. Students will write remainders in two ways to create equivalent polynomial expressions and determine whether a given expression is a factor according to the Polynomial Remainder Theorem. Both factoring and long division will be used in upcoming tasks to write polynomials in factored form and to find their roots
Guided notes for class use on remainder theorem and factors.
The task has students use the remainder theorem to deduce a linear factor of a cubic polynomial, and then to completely factor the polynomial. Students will need some procedure (e.g., synthetic or long division, or guess-and-check the coefficients) for determining the quadratic factor. Having the factored form permits students to deduce much about the structure of the graph.
This video goes over the Polynomial Remainder Theorem.
This video goes over the proof of the Remainder Theorem.
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Students apply the remainder theorem and understand the role zeros play in the theorem.
Practice using the Remainder Theorem.
This power point Explains the Remainder and Factor Theorems
This tutorial covers dividing a polynomial by a binomial of the form x-c using synthetic division, using the Remainder Theorem in conjunction with synthetic division to find a functional value, and using the Factor theorem in conjunction with synthetic division to find factors and zeros of a polynomial function.
This video finds the remainder of (-3x^3-4x^2+10x-7) divided by (x-2) using the PRT (Polynomial Remainder Theorem).