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
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Favorites (5)
 
Resources (18)
 
Reflections (1)
pythagorean triplesresized
   

Review of Polynomial Roots and Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Favorites (2)
 
Resources (10)
waterfall trivia
   

The Remainder Theorem

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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).

 
Favorites (3)
 
Resources (13)
 
Reflections (1)
remainder theorem exit
   

Quiz and Intro to Graphs of Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.

 
Favorites (3)
 
Resources (12)
 
Reflections (1)
quartic
   

That's Fundamental

Algebra II » Unit: Complex Numbers
Algebra II » Unit: Complex Numbers
Merrie Rampy
Craigmont, ID
Environment: Rural
 
Big Idea:

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

 
Favorites (1)
 
Resources (10)
 
Reflections (1)
fundamental theorem
   

Seeing Structure in Expressions - Factoring Higher Order Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Favorites (5)
 
Resources (25)
 
Reflections (2)
factoring quick poll
   

Polynomial Long Division and Solving Polynomial Equations

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Operations with polynomials are a lot like operations with integers.

 
Favorites (6)
 
Resources (22)
 
Reflections (1)
long
   

The Fundamental Theorem of Algebra

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

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

 
Favorites (4)
 
Resources (13)
 
Reflections (2)
cubic graph
   

Higher Degree Polynomials, Day 1 of 2

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

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

 
Favorites (6)
 
Resources (12)
 
Reflections (1)
polynomialdeg4
   

The Fundamental Theorem of Algebra and Imaginary Solutions

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Resources (14)
 
Reflections (1)
quadratic imaginary
   

Polynomial Practice & Review

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

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

 
Favorites (2)
 
Resources (12)
polynomial graph
   

Arithmetic with Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.

 
Favorites (4)
 
Resources (23)
 
Reflections (2)
mandlebrot set
   

Complex Number Battleship

Algebra II » Unit: Games
Algebra II » Unit: Games
Merrie Rampy
Craigmont, ID
Environment: Rural
 
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!

 
Favorites (3)
 
Resources (9)
battleship
   

Performance Task - Representing Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Favorites (2)
 
Resources (15)
 
Reflections (1)
representing polynomials
   

Polynomial and Rational Functions: Unit Assessment

12th Grade Math » Unit: Polynomial and Rational Functions
12th Grade Math » Unit: Polynomial and Rational Functions
Tim  Marley
Troy, MI
Environment: Suburban
 
Big Idea:

Assess students' understanding of polynomial and rational functions.

 
Favorites (2)
 
Resources (3)
images
Common Core Math
 
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