HSA-APR.B.3

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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.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.

83 Lesson(s)

### Quadratic Functions: Standard and Intercept Forms

Algebra II »
Unit: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Big Idea:

#### Quadratic functions are graphed as parabolas; how we go about creating the graph depends on which form the function is written in.

Standards:

Favorites
(8)

Resources
(21)

Reflections
(1)

### Three Methods of Solving Quadratics and Word Problems

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### The structure of a quadratic equation can help students determine how to solve the equation.

Standards:

Favorites
(3)

Resources
(15)

Reflections
(1)

### Finding Roots of All Sorts

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### In this fast-paced lesson, students are introduced to as many ideas as they can handle, while also being given space to make their own sense of those ideas.

Favorites
(3)

Resources
(24)

Reflections
(1)

### 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
(4)

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
(3)

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
(2)

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)

Big Idea:

#### In many cases, polynomial functions are ideal mathematical models that support quantitative and abstract reasoning.

Standards:

Favorites
(3)

Resources
(12)

Reflections
(1)

### Catch the Mistake

12th Grade Math »
Unit: Midterm Review and Exam

12th Grade Math »
Unit: Midterm Review and Exam

Big Idea:

#### Mathematical Practice 3 takes center stage as students critique the reasoning of others for problematic questions.

Standards:

Resources
(9)

### 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)

### Area Models for Multiplying Polynomials and Factoring Quadratic Expressions

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### This fast-paced lesson introduces multiplication of binomials and factoring of quadratic expressions for the first time, which sets students up to explore both in depth over the next few days.

Standards:

Favorites
(11)

Resources
(22)

Reflections
(1)

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