CMS Curriculum Guides 2011-2012
Algebra II
Unit Title:
Polynomial Functions and Operations
Unit Title: Time:
Suggested
Suggested Timeline:
15 days
Enduring understanding (Big Idea): Factor polynomials in multiple forms, analyze polynomial functions
and their graphs by identifying end behavior and roots, graph polynomial functions and inverses
Essential Questions: How are factors and roots of a polynomial equation related? How are a function
and its inverse function related?
Common Core Standards
Mathematical Textbook
Practices
Alignment

A-SSE.1. Interpret expressions that
represent a quantity in terms of its
★
context.
1, 2,3
1-1
o
Interpret parts of an expression, such as
terms, factors, and coefficients.
Connection to 2003 Standards
Interpret complicated expressions by
viewing one or more of their parts as a
single entity. For example, interpret
P(1+r)n as the product of P and a factor
not depending on P.

A-SSE.2. Use the structure of an
expression to identify ways to rewrite it.
For example, see x4 – y4 as (x2)2 – (y2)2,
thus recognizing it as a difference of
squares that can be factored as (x2 –
y2)(x2 + y2).
7
4-4, 4-5, 4-6,
4-7

A-APR.1. Understand that polynomials
form a system analogous to the
integers, namely, they are closed under
the operations of addition, subtraction,
and multiplication; add, subtract, and
multiply polynomials.
1
5-3, 5-4

A-APR.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).
1
*See 5-4
Remainder
Theorem

A-APR.3. Identify zeros of polynomials
when suitable factorizations are
available, and use the zeros to construct
4
*See 5-2
problem 2, 3
1.03 Operate with algebraic
expressions (polynomial, rational,
complex fractions) to solve
problems.
CMS Curriculum Guides 2011-2012
Algebra II
a rough graph of the function defined
by the polynomial.

A-APR.4. Prove polynomial identities
and use them to describe numerical
relationships. For example, the
polynomial identity (x2 + y2)2 = (x2 – y2)2
+ (2xy)2 can be used to generate
Pythagorean triples.
2, 3
5-5, 5-6

A-APR.5. (+) Know and apply the
Binomial Theorem for the expansion of
(x + y)n in powers of x and y for a
positive integer n, where x and y are
any numbers, with coefficients
determined for example by Pascal’s
Triangle.1
1
5-7
F-IF.7. Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
★
cases.
4
5-1, 5-2
o
c. Graph polynomial functions,
identifying zeros when suitable
factorizations are available, and
showing end behavior.

F-IF.8. Write a function defined by an
expression in different but equivalent
forms to reveal and explain different
properties of the function.
o
a. Use the process of factoring and
completing the square in a quadratic
function to show zeros, extreme values,
and symmetry of the graph, and
interpret these in terms of a context.

F-BF.4. Find inverse functions.
o
Solve an equation of the form f(x) = c
for a simple function f that has an
inverse and write an expression for the
inverse. For example, f(x) =2 x3 or f(x) =
(x+1)/(x–1) for x ≠ 1.
o
(+) Verify by composition that one
function is the inverse of another.
o
(+) Read values of an inverse function
from a graph or a table, given that the
2.06 Use cubic equations to model
and solve problems.
a.
Solve using tables and
graphs.
Interpret constants and coefficients
in the context of the problem.
4, 8
5-8
1
6-6, 6-7
2.01 Use the composition and
inverse of functions to model and
solve problems; justify results.
CMS Curriculum Guides 2011-2012
Algebra II
function has an inverse.
(+) Produce an invertible function from
a non-invertible function by restricting
the domain.
Prior Knowledge: Solving equations, basic
quadratic factoring, graphing quadratic functions
Key Vocabulary
Discriminant, Greatest Common Factor,
Quadratic Formula, End Behavior, Relative
Maximum, Relative Minimum, Turning, Point,
Synthetic Division, Composite Function, Inverse
Function
Resources:

Pearson Algebra II Dynamic Activities (log in to pearsonsuccessnet.com and access the
Interactive Digital Path): 4-4, 4-5, 4-6, 4-7, 5-2, 5-4

Problem-Based Task:


o
Chapter 4 Tasks : Task 3 only
o
Chapter 5 Tasks
o
Chapter 6 Tasks : Tasks 3 and 4 only
PowerAlgebra.com, Teacher Online Access pack, Algebra 2 Companion – vocabulary, key
concepts, got it?
Honors – see Challenge problems at the end of sections, advanced level assignments, dynamic
activities, enrichment worksheets, extended concept bytes
o 4-5 Enrichment
o 4-7 Enrichment
o Chapter 5 Project
o Chapter 6 Project