Curriculum  /  Math  /  11th Grade  /  Unit 3: Polynomials  /  Lesson 7

Polynomials

Lesson 7

Math

Unit 3

11th Grade

Lesson 7 of 14

Objective

Divide polynomials by binomials to determine linear factors.

Common Core Standards

Core Standards

  • A.APR.A.1 — Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
  • A.APR.B.2 — Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
  • A.APR.B.3 — Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Foundational Standards

  • A.REI.A.1
  • A.REI.B.3

Criteria for Success

  1. Describe that just like with the operations of multiplication, addition, and subtraction, polynomial division follows the same principles as integer division.
  2. Divide binomials into polynomials using long division.
  3. Identify that when the remainder of this division is zero, the binomial is a factor of the polynomial.

Tips for Teachers

In this lesson, students will focus on long division and not be introduced to synthetic division. For more information about reasoning for this, see the Algebra Progressions for the Common Core, page 9. Lane Walker also provides some additional reasoning on the topic. She addresses the topic again in this post.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Find the product.

$${(x-3)(x^2-2x+3)}$$

Once we find the product, how would we work backwards to get both factors again?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

What is the other factor you would multiply $${x-2}$$ by to get the polynomial $${x^4-4x^2-5x+10}$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Target Task

5-10 minutes

Problem 1

One factor of the polynomial $${2x^4+2x^3+3x+3}$$ is $${(x+1)}$$. What is the other factor?

Problem 2

How can you confirm that $${x+1}$$ is indeed a factor of $${2x^4+2x^3+3x+3}$$ through the long division?

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students are given the graph of the polynomial function (with an integer root), the equation, and they need to identify one linear factor from the root and then show this as a factor through long division. 
  • Include problems where students are given the roots and they need to test one of the factors through long division.

Next

Determine if a binomial is a factor of a polynomial using the remainder theorem.

Lesson 8
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Polynomial Features and Graphs

Topic B: Operations with Polynomials

Topic C: Polynomial Extensions

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free