HSA-APR.B.2

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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.

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## 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

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)

### Uses of Polynomial Division- The Factor and Remainder Theorems

Algebra II »
Unit: Polynomial Functions

Algebra II »
Unit: Polynomial Functions

Big Idea:

#### Show students why polynomial division is useful in the lesson.

Standards:

Favorites
(4)

Resources
(28)

Reflections
(1)

### 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
(3)

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)

### Surface Area and Volume Functions

12th Grade Math »
Unit: Cubic 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.

Standards:

Favorites
(2)

Resources
(12)

### Roots and Graphs of Cubic Functions

12th Grade Math »
Unit: 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

Standards:

Favorites
(1)

Resources
(12)

Reflections
(1)

### More Surface Area and Volume Functions and the Painted Cube Problem

12th Grade Math »
Unit: Cubic Functions

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?

Standards:

Favorites
(3)

Resources
(11)

### 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)

### 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)

### Graphs of Cubic Functions

12th Grade Math »
Unit: 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.

Standards:

Favorites
(1)

Resources
(10)

### Higher Degree Polynomials, Day 2 of 2

Algebra II »
Unit: Higher-Degree Polynomials

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.

Standards:

Favorites
(2)

Resources
(14)

Big Idea:

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

Standards:

Favorites
(1)

Resources
(17)

Reflections
(2)

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