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Algebra II

(7 Units, 80 Lessons)

Unit 4 - Polynomial Theorems and Graphs(15 Lessons)

Seeing Structure in Expressions - Factoring Higher Order Polynomials

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.

25 Resources

6 Favorites

25 Resources

6 Favorites

Proving Polynomial Identities

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.

18 Resources

8 Favorites

18 Resources

8 Favorites

Polynomial Long Division and Solving Polynomial Equations

Algebra II

» Unit:

Polynomial Theorems and Graphs

Big Idea:Operations with polynomials are a lot like operations with integers.

22 Resources

7 Favorites

22 Resources

7 Favorites

The Remainder Theorem

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).

13 Resources

5 Favorites

13 Resources

5 Favorites

The Fundamental Theorem of Algebra and Imaginary Solutions

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.

14 Resources

0 Favorites

14 Resources

0 Favorites

Arithmetic with Complex Numbers

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.

23 Resources

7 Favorites

23 Resources

7 Favorites

Review of Polynomial Roots and Complex Numbers

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.

10 Resources

2 Favorites

10 Resources

2 Favorites

Quiz and Intro to Graphs of Polynomials

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.

12 Resources

4 Favorites

12 Resources

4 Favorites

Graphing Polynomials - End Behavior

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.

15 Resources

10 Favorites

15 Resources

10 Favorites

Graphing Polynomials - Roots and the Fundamental Theorem of Algebra

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.

20 Resources

9 Favorites

20 Resources

9 Favorites

Analyzing Polynomial Functions

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."

16 Resources

4 Favorites

16 Resources

4 Favorites

Quiz on Graphing Polynomials and Intro to Modeling with Polynomials

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.

11 Resources

1 Favorites

11 Resources

1 Favorites

Performance Task - Representing Polynomials

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.

15 Resources

6 Favorites

15 Resources

6 Favorites

Review of 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.

16 Resources

1 Favorites

16 Resources

1 Favorites

Unit Assessment: 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.

5 Resources

2 Favorites

5 Resources

2 Favorites