Algebra 2‎ > ‎

Ch 8 - Polynomials

Click here for Parent Guide with Extra Practice for Chapter 8 - Polynomials from CPM

Chapter

 Objective

Students will be able to…

Standard(s)

Help/Examples

 Practice

8.1.1

Describe the graph of a polynomial given its equation in factored form

A-APR.3

F-IF.4

F-IF.7c

 

Polynomial end behavior

Polynomial end behavior example

 

8.1.2

Consolidate, generalize the graph of a polynomial given its equation in factored form

A-APR.3

F-IF.7c

Determine the x-intercepts of a polynomial function by analyzing its factors

Determine the end behavior of a graph by analyzing its equation

Determine when a polynomial function changes sign

Sketch the graph of a higher degree polynomial

Determine the equation of a polynomial by analyzing its graph

 

8.1.3

Write exact equations for the graphs of polynomial functions given the x‑intercepts and one additional point

A-APR.3

F-IF.4

F-IF.7c

 

Writing Polynomial Equations given the Zeros of the Functions

 

8.2.1

Solve equations using imaginary and complex numbers

N-CN.1

N-CN.7

N-CN.9 (+)

 

Introduction to i and imaginary numbers

Imaginary roots of negative numbers

Introduction to complex numbers
https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/e/the-imaginary-unit-and-complex-numbers

8.2.2

Write the equations for quadratic functions given the roots

N-CN.1

N-CN.7

N-CN.8 (+)

N-CN.9 (+)

 

Write a Polynomial Function with Complex Zeros

 

8.2.2

Practice operations with complex numbers

N-CN.2

 

Calculating i raised to arbitrary exponents

Adding complex numbers

Subtracting complex numbers

Multiplying complex numbers

Dividing complex numbers

 

Imaginary unit powers

Adding and subtracting complex numbers

Multiplying complex numbers

Dividing complex numbers

8.2.3

Use the complex plane as a way to visualize complex numbers and complex roots for quadratic functions

N-CN.1

N-CN.7

N-CN.9 (+)

 

Plotting complex numbers on the complex plane

 

8.2.3

Calculate the absolute value of a complex number

N-CN.2

 

Absolute value of a complex number

 

Absolute value of complex numbers

8.3.1

use polynomial division to find factors of polynomials

A-APR.2

A-APR.6

N-CN.9 (+)

 

Polynomial division

Dividing polynomials 1

Dividing polynomials with remainders

Synthetic division

Synthetic division example 2

 

8.3.2

Use the Integral Zero Theorem, polynomial division and the Factor Theorem to find integral roots and to find all roots of polynomials with degree greater than two

A-SSE.2

A-APR.2

A-APR.3

A-APR.6

F-IF.7c

N-CN.8 (+)

N-CN.9 (+)

 

Example: Factoring a fourth degree expression

Factoring 5th degree polynomial to find real zeros

Identifying graph based on roots

 

Using zeros to graph polynomials

 8.3.3

Use knowledge of polynomial functions and graphs to maximize volume of a tank

A-APR.2

A-APR.3

A-APR.6

F-IF.5

F-IF.7c

N-CN.9 (+)

 

 

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