Rational Roots and Remainders: Important Theorems of Polynomials

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Objective

SWBAT identify the connections between dividing polynomials and evaluating polynomials and determine the possible rational zeros of a polynomial using the Rational Root Test.

Big Idea

Using polynomial division students discover the Remainder Theorem & then learn about the Rational Root Test.

Warm-up: Polynomial Division

7 minutes

Students should begin working on the two polynomial division problems on page 2 of the Flipchart  on a scratch piece of paper (they will record their findings later). After about 5 minutes, I plan to go over the first problem using whichever method (long division, synthetic division, or division with generic squares) that students request, maybe even all 3.

Explanation: Remainder Theorem, Factor Theorem, and Rational Root test

25 minutes
Remainder thm, Factor thm, and Rational Root Test.pptx page 1
Remainder thm, Factor thm, and Rational Root Test.pptx page 2
Remainder thm, Factor thm, and Rational Root Test.pptx page 3
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Remainder thm, Factor thm, and Rational Root Test.pptx page 10
Remainder thm, Factor thm, and Rational Root Test.pptx page 11

Closure: 3-2-1 Assessment

5 minutes

Today was the last day of new learning and I definitely plan on sharing this with students. So for the next week students are just going to be presented with opportunities to put all the pieces together and build on their current knowledge. Since we are getting close to the end of the unit, I wanted to get a sense for how students feel that they are progressing. At the end of today’s lesson I am going to have my students complete a 3-2-1 Assessment to accomplish this. The prompts for students are on the last slide of the power point. We will be reviewing students’ responses at the start of class tomorrow and may use some of their feedback to drive the instruction in the upcoming lessons.

Homework

1 minutes

Assign Homework 6 - Polynomials for homework.