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- HSA-APR.B.2Know 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).
- HSA-APR.B.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

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.

Uses of Polynomial Division- The Factor and Remainder Theorems

Algebra II

» Unit:

Polynomial Functions

Big Idea:Show students why polynomial division is useful in the lesson.

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.

Surface Area and Volume Functions

12th Grade Math

» Unit:

Cubic Functions

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.

Roots and Graphs of Cubic Functions

12th Grade Math

» Unit:

Cubic Functions

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

More Surface Area and Volume Functions and the Painted Cube Problem

12th Grade Math

» Unit:

Cubic Functions

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

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.

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.

Graphs of Cubic Functions

Algebra II

» Unit:

Cubic Functions

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

Graphs of Cubic Functions

12th Grade Math

» Unit:

Cubic Functions

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.

Higher Degree Polynomials, Day 2 of 2

Algebra II

» Unit:

Higher-Degree Polynomials

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

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).

HSA-APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.