The Complex Number System
HSN-CN.C.9
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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^{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.
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HSN-CN.C.9
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
27 Lesson(s)
Proving Polynomial Identities
Algebra 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.
Standards:
Favorites
(5)
Resources
(18)
Reflections
(1)
Review of Polynomial Roots and Complex Numbers
Algebra 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.
Standards:
Favorites
(2)
Resources
(10)
The Remainder Theorem
Algebra 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).
Standards:
Favorites
(4)
Resources
(13)
Reflections
(1)
Quiz and Intro to Graphs of Polynomials
Algebra 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.
Standards:
Favorites
(3)
Resources
(12)
Reflections
(1)
Big Idea:
Let your students have the fun of confirming the Fundamental Theorem of Algebra and they'll remember it a lot longer!
Standards:
Favorites
(1)
Resources
(10)
Reflections
(1)
Seeing Structure in Expressions - Factoring Higher Order Polynomials
Algebra 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.
Standards:
Favorites
(5)
Resources
(25)
Reflections
(2)
Polynomial Long Division and Solving Polynomial Equations
Algebra 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.
Standards:
Favorites
(6)
Resources
(22)
Reflections
(1)
The Fundamental Theorem of Algebra
Algebra II »
Unit: Higher-Degree Polynomials
Algebra II »
Unit: Higher-Degree Polynomials
Big Idea:
Just how many solutions does this polynomial have?! Exactly the same number as its degree!
Standards:
Favorites
(4)
Resources
(13)
Reflections
(2)
Higher Degree Polynomials, Day 1 of 2
Algebra II »
Unit: Higher-Degree Polynomials
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.
Standards:
Favorites
(6)
Resources
(12)
Reflections
(1)
The Fundamental Theorem of Algebra and Imaginary Solutions
Algebra 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.
Standards:
Resources
(14)
Reflections
(1)
Polynomial Practice & Review
Algebra II »
Unit: Higher-Degree Polynomials
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.
Standards:
Favorites
(2)
Resources
(12)
Arithmetic with Complex Numbers
Algebra 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.
Standards:
Favorites
(5)
Resources
(23)
Reflections
(2)
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!
Standards:
Favorites
(3)
Resources
(9)
Performance Task - Representing Polynomials
Algebra 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.
Standards:
Favorites
(2)
Resources
(15)
Reflections
(1)
Polynomial and Rational Functions: Unit Assessment
12th Grade Math »
Unit: Polynomial and Rational Functions
12th Grade Math »
Unit: Polynomial and Rational Functions
Big Idea:
Assess students' understanding of polynomial and rational functions.
Standards:
Favorites
(2)
Resources
(3)
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