Algebra 2 Lesson Plan

Unit Correlation to ARRC:  Pre-AP Unit 6: Polynomial Expressions and Equations

Lesson Title: Unit 6.3 Theorems, Factors, and Roots                 

Lesson Date: December

Lesson TEKS

Focus TEKS:

2A.7B add, subtract, and multiply polynomials (S) R.C. 1

2A.7C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two (S) R.C. 1

2A.7D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods (S) R.C. 1

2A.7E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping (R) R.C. 1

Ongoing TEKS:

2A.7I write the domain and range of a function in interval notation, inequalities, and set notation (S) R.C. 1

Learning Targets

Student will know...

  • the Fundamental Theorem of Algebra.
  • the Remainder Theorem
  • Rational Roots Theorem

Student will be able to...

  • use the graph of a polynomial function to find one or more factors.
  • use the graph of a polynomial function to determine the nature of its roots.
  • add, subtract, multiply, and divide polynomials in mathematical and real world situations.
  • determine the quotient of two polynomials by long and synthetic division.
  • Find the factors of a polynomial function using various methods
  • Find the remainder of a polynomial function using synthetic division

Criteria for Success

  • I can determine whether a binomial is a factor of a polynomial by using synthetic division - does it have a remainder (previous lessons)
  • I can determine the number of roots for a polynomial equation.
  • I can identify possible rational zeros of a polynomial function.
  • I can find the zeros of a polynomial function by factoring or dividing.

Performance of Understanding

  • Theorems/Question Stem Matching Activity
  • ClassKick Activity
  • Desmos Activity

Scaffolding/Discussion Questions

Lesson Outline

  1. Identify and explain:
  1. Degree
  2. Factor
  3. Synthetic Division (Substitution)
  4. Conjugate Root Theorem
  5. Factor Theorem
  6. Remainder Theorem
  7. Fundamental Theorem of Algebra
  8. Rational Root Theorem
  1. How can we use these theorems to analyze (number of roots, possible roots, factors, and actual roots of a polynomial?
  2. How does a graph support the work of finding factors and roots?

  1. Warm-Up: Student Partners: Define theorems while matching them to types of question stems (compare/contrast, analysis, evaluation)
  2. Teacher Directed: Demonstrate examples analyzing polynomials for factors/roots
  3. Student Activity: on ClassKick analyze 4  polynomials for factors, roots, and graph.
  4. Student Partners: work through Desmos activity to build fluency in understanding the application of the theorems (application, analysis); Class Discussion of these questions
  5. Homework: 12 polynomials to analyze

Critical Thinking Questions

Resources Needed

Technology Used

  • How are x-intercepts, roots, factors, and solutions related?
  • If all the possible zeros of a polynomial are integers, what do you know about its leading coefficient?
  • In what ways do you use the theorems in this lesson to solve polynomials?
  • Handouts
  • ClassKick Activity
  • Desmos Activity

  • ClassKick
  • Desmos

Formative Assessment

Homework

Informal observation of discussion

Review of work on ClassKick

Review of work on Desmos

Quiz on next class day

Handout - 12 polynomials to analyze