HSA-APR.C.4

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

 
29 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
   

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 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
   

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 (5)
 
Resources (23)
 
Reflections (2)
mandlebrot set
   

Unit Test: Sequences and Series

Algebra II » Unit: Sequences and Series
Algebra II » Unit: Sequences and Series
Jarod Hammel
Huntington, IN
Environment: Suburban
 
Big Idea:

Test Time!

 
Resources (9)
 
Reflections (1)
desks
   

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
   

Prove It

Algebra II » Unit: Algebraic Arithmetic
Algebra II » Unit: Algebraic Arithmetic
Merrie Rampy
Craigmont, ID
Environment: Rural
 
Big Idea:

Show your students that they really can "prove it" with this lesson on polynomial identities.

 
Favorites (1)
 
Resources (10)
 
Reflections (1)
prove it
   

Graphing Polynomials - End Behavior

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

 
Favorites (7)
 
Resources (15)
 
Reflections (1)
warm up end behavior
   

Use It

Algebra II » Unit: Algebraic Arithmetic
Algebra II » Unit: Algebraic Arithmetic
Merrie Rampy
Craigmont, ID
Environment: Rural
 
Big Idea:

First you create it, then you use it...this lesson allows students to use the polynomial identities they just proved.

 
Resources (14)
 
Reflections (1)
use it1
   

Graphing Polynomials - Roots and the Fundamental Theorem of Algebra

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

 
Favorites (6)
 
Resources (20)
 
Reflections (1)
polynomial graph sort
   

Egyptian Fractions

Algebra II » Unit: Rational Functions
Algebra II » Unit: Rational Functions
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Egyptian fractions provide an interesting arena for putting rational functions to use.

 
Resources (9)
eye of horus bw
Common Core Math
 
Something went wrong. See details for more info
Nothing to upload
details
close