Algebra II
(7 Units, 80 Lessons)
Unit 4 - Polynomial Theorems and Graphs(15 Lessons)
Seeing Structure in Expressions - Factoring Higher Order PolynomialsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Like quadratic expressions, some higher order polynomial expressions can be rewritten in factored form to reveal values that make the expression equal to zero.
Proving Polynomial IdentitiesAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:There are links between polynomials and geometry. Both branches of math use proof and a polynomial identity can be used to generate Pythagorean triples.
Polynomial Long Division and Solving Polynomial EquationsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Operations with polynomials are a lot like operations with integers.
The Remainder TheoremAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Any polynomial p(x) can be written as a product of (x – a) and some quotient q(x), plus the remainder p(a).
The Fundamental Theorem of Algebra and Imaginary SolutionsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:The degree of a polynomial equation tells us how many solutions to expect as long as we include both real and imaginary solutions.
Arithmetic with Complex NumbersAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.
Review of Polynomial Roots and Complex NumbersAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.
Quiz and Intro to Graphs of PolynomialsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.
Graphing Polynomials - End BehaviorAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:A good sketch of a polynomial function can be produced by considering the end-behavior, roots and y-intercept of a polynomial function.
Graphing Polynomials - Roots and the Fundamental Theorem of AlgebraAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:A good sketch of a polynomial function can be produced by considering the end-behavior, roots and y-intercept of a polynomial function.
Analyzing Polynomial FunctionsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Polynomial functions behave differently over different values of input. We can characterize this behavior using terms like "increasing," "decreasing," "minimum," and "maximum."
Quiz on Graphing Polynomials and Intro to Modeling with PolynomialsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Polynomials can be used to model some real world situations like maximizing volume; graphing polynomial functions can help us understand the model.
Performance Task - Representing PolynomialsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:The graphs of polynomial functions can be transformed by altering the algebraic form in specific ways. These transformations have the same effect on all the function types studied in Algebra 2 and Precalculus.
Review of Polynomial Theorems and GraphsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:Getting ready for a summative test on polynomial theorems and graphs means doing lots of problems and asking questions when you get stuck.
Unit Assessment: Polynomial Theorems and GraphsAlgebra II » Unit:Polynomial Theorems and Graphs
Algebra II
» Unit:
Polynomial Theorems and Graphs
Big Idea:This written assessment is students' chance to show that they can work flexibly with polynomial operations, sketch and interpret graphs of polynomial functions and understand two important polynomial theorems.
