HSA-APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

 
47 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
   

Uses of Polynomial Division- The Factor and Remainder Theorems

Algebra II » Unit: Polynomial Functions
Algebra II » Unit: Polynomial Functions
Amelia Jamison
Caldwell, ID
Environment: Rural
 
Big Idea:

Show students why polynomial division is useful in the lesson.

 
Favorites (4)
 
Resources (28)
 
Reflections (1)
image uses of polynomial division
   

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
   

Surface Area and Volume Functions

12th Grade Math » Unit: Cubic Functions
12th Grade Math » Unit: Cubic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

How do the surface area and volume of a prism change as the prism grows? Students build prisms and use these prisms to generate quadratic and cubic functions.

 
Favorites (2)
 
Resources (12)
the painted cube
   

Roots and Graphs of Cubic Functions

12th Grade Math » Unit: Cubic Functions
12th Grade Math » Unit: Cubic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Rather than giving students functions or graphs, ask them to generate their own functions and graphs to fit descriptions. This makes students the authors of the problems--and engages them in a different level of critical thinking, while giving them the cha

 
Favorites (1)
 
Resources (12)
 
Reflections (1)
screenshot 2014 05 13 15 20 51
   
12th Grade Math » Unit: Cubic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Build prisms that fit certain requirements and generate functions to describe these prisms. What kinds of functions arise?

 
Favorites (3)
 
Resources (11)
the painted cube day 2
   

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
   

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
   

Graphs of Cubic Functions

12th Grade Math » Unit: Cubic Functions
12th Grade Math » Unit: Cubic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

What connections can you make between the graphs of cubic functions and their equations? Students complete a matching activity to help them develop a more abstract understanding of these functions.

 
Favorites (1)
 
Resources (10)
screenshot 2014 05 13 15 19 19
   

Higher Degree Polynomials, Day 2 of 2

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

Students test their mettle against polynomial challenges, comparing graphs to tables and doing long division with unknown coefficients.

 
Favorites (2)
 
Resources (14)
polynomialdeg5
   

Graphs of Cubic Functions

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

How many points does it take to determine a cubic function? Four - and it helps if three of them are roots!

 
Favorites (1)
 
Resources (17)
 
Reflections (2)
graphs of cubics image
Common Core Math
 
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