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- HSN-CN.C.7Solve quadratic equations with real coefficients that have complex solutions.
- HSN-CN.C.8(+) Extend polynomial identities to the complex numbers. For example, rewrite x<sup>2</sup> + 4 as (x + 2i)(x – 2i).
- HSN-CN.C.9(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

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.

Colleen Werner

Suburban Env.

18 Resources

7 Favorites

18 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.

Colleen Werner

Suburban Env.

10 Resources

2 Favorites

10 Resources

2 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).

Colleen Werner

Suburban Env.

13 Resources

5 Favorites

13 Resources

5 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.

Colleen Werner

Suburban Env.

12 Resources

3 Favorites

12 Resources

3 Favorites

That's Fundamental

Algebra II

» Unit:

Complex Numbers

Big Idea:Let your students have the fun of confirming the Fundamental Theorem of Algebra and they'll remember it a lot longer!

Merrie Rampy

Rural Env.

10 Resources

1 Favorite

10 Resources

1 Favorite

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.

Colleen Werner

Suburban Env.

25 Resources

6 Favorites

25 Resources

6 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.

Colleen Werner

Suburban Env.

22 Resources

7 Favorites

22 Resources

7 Favorites

The Fundamental Theorem of Algebra

Algebra II

» Unit:

Higher-Degree Polynomials

Big Idea:Just how many solutions does this polynomial have?! Exactly the same number as its degree!

Jacob Nazeck

Suburban Env.

13 Resources

4 Favorites

13 Resources

4 Favorites

Higher Degree Polynomials, Day 1 of 2

Algebra II

» Unit:

Higher-Degree Polynomials

Big Idea:Applying the Remainder Theorem and the Fundamental Theorem of Algebra, students explore the graphs of higher-degree polynomials.

Jacob Nazeck

Suburban Env.

12 Resources

6 Favorites

12 Resources

6 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.

Colleen Werner

Suburban Env.

14 Resources

14 Resources

Polynomial Practice & Review

Algebra II

» Unit:

Higher-Degree Polynomials

Big Idea:Polynomial functions have a predictable number of zeros and we can find them with technology, synthetic substitution, or factoring.

Jacob Nazeck

Suburban Env.

12 Resources

2 Favorites

12 Resources

2 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.

Colleen Werner

Suburban Env.

23 Resources

5 Favorites

23 Resources

5 Favorites

Complex Number Battleship

Algebra II

» Unit:

Games

Big Idea:Use games like this to fill those odd days before break or during homecoming week with meaningful mathematical activities or use for fun review!

Merrie Rampy

Rural Env.

9 Resources

5 Favorites

9 Resources

5 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.

Colleen Werner

Suburban Env.

15 Resources

2 Favorites

15 Resources

2 Favorites

Polynomial and Rational Functions: Unit Assessment

12th Grade Math

» Unit:

Polynomial and Rational Functions

Big Idea:Assess students' understanding of polynomial and rational functions.

Tim Marley

Suburban Env.

3 Resources

2 Favorites

3 Resources

2 Favorites

HSN-CN.C.7

Solve quadratic equations with real coefficients that have complex solutions.

HSN-CN.C.8

(+) Extend polynomial identities to the complex numbers. For example, rewrite x^{2} + 4 as (x + 2i)(x – 2i).

HSN-CN.C.9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.