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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.

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.

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).

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.

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!

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.

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.

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!

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.

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.

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.

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.

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!

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.

Polynomial and Rational Functions: Unit Assessment

12th Grade Math

» Unit:

Polynomial and Rational Functions

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

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.