Progressive Mathematics Initiative
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Mathematics Curriculum
Unit Plan # 2
Title: Polynomial Functions
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: The unit begins with reviewing rules of exponents, adding, subtracting, and multiplying
polynomials. Dividing polynomials and the Remainder Theorem are emphasized. Students will be asked to
analyze polynomial functions and find the zeros both algebraically, in tables, and graphically. Students will
also be asked to write polynomial functions from the given zeros.
Learning Targets
Conceptual Category: Number and Quantity Domain: The Complex Number System
Cluster: Perform arithmetic operations on polynomials
Know there is a complex number 𝑖 such that 𝑖 2 = – 1, and every complex number has the
form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.
N-CN.8
Extend polynomials identities to the complex numbers. For example, rewrite 𝑥 2 + 4 as
(𝑥 + 2𝑖)(𝑥 − 2𝑖).
Conceptual Category: Algebra Domain: Arithmetic with Polynomials and Rational Expressions
N-CN.1
Cluster: Use complex numbers in polynomial identities and equations
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.
Cluster: Understand the relationship between zeros and factors of polynomials
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).
A-APR.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.
Cluster: Use polynomials identities to solve problems
A-APR.2
Prove polynomial identities and use them to describe numerical relationships. For
example, the polynomial identity (𝑥 2 + 𝑦 2 )2 = (𝑥 2 − 𝑦 2 ) + (2𝑥𝑦)2 can be used to generate
Pythagorean triples.
A-APR.5
Know and apply the Binomial Theorem for the expansion of (𝑥 + 𝑦)𝑛 in powers of x and y
for positive integer n, where x and y are any numbers, with coefficients determined for
example by Pascal’s Triangle. 1
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +
A-APR.6
r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than
the degree of b(x), using inspection, long division, or, for the more complicated examples,
a computer algebra system. (Fluency)
Conceptual Category: Algebra Domain: Seeing Structure in Expressions
A-APR.4
Cluster: Interpret the structure of expressions
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).
Algebra II – Polynomial Functions
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NJCTL.org
A-SSE.3
Choose and produce an equivalent form of an expression to reveal and explain properties
of the quantity represented by the expression.★
Cluster: Reasoning with Equations and Inequalities
A-REI.11
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and
y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic functions.★ (For this unit, linear,
polynomial and absolute value only.)
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
F-IF.4
For a function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. Key features include: intercepts; intervals
where the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.★
Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases
Unit Essential Question:
Unit Enduring Understandings:
 How are factors, zeros and x-intercepts related for
 Like terms have the same bases with the
a polynomial function?
same degrees.
 Graphs of polynomials have end behaviors
 Does knowing the zeros of a function give you
dependent on the degree and leading
enough information to sketch it?
coefficient of the polynomial
 Division of Polynomials follow the rules of long
division
 The total number of zeros (real and imaginary)
is equal to the degree of the polynomial.
Unit Objectives:
 Students will be able to combine polynomial functions using operations of addition, subtraction,
multiplication, and division and will be fluent in factoring all types of polynomials.
 Students will know and be able to apply the Remainder Theorem.
 Students will be to describe characteristics of polynomials given equations, tables, and graphs.
 Students will be able to find the zeros of a polynomial, both real and imaginary.
 Students will be able to write polynomials from its given zeros.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 4 Quizzes
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Timeframe
F-IF.7
Topic #1: Properties of Exponents Review
Topic #2: Operations with Polynomials Review
Quiz 1 Exponents, Addition, Subtraction and
Multiplication of Polynomials
Topic #3: Special Binomial Products
Topic #4: Binomial Theorem
Algebra II – Polynomial Functions
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Topic #5: Factoring Polynomials Review
Quiz 2 Special Binomial Products, Binomial
Theorem, Factoring
Topic #6: Dividing Polynomials
Quiz 2 Dividing Polynomials and the Remainder
Theorem
Topic #7: Polynomial Functions
Lab: Exploration of the Values of Terms in a
Polynomial
Lab: Polynomials Discovery
Topic #8: Analyzing Graphs and Tables of
Polynomials
Quiz 3 Characteristics of Polynomials
Topic #9: Zeros and Roots of Polynomial Functions
Topic #10: Writing Polynomials from its Zeros
Quiz 4 Analyzing Graphs and Tables of
Polynomials and Roots of Polynomial
Functions
Topic #11: Review and Unit Test
Curriculum Resources:
 www.njctl.org/courses/math/algebra2/
 www.geogebra.org
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Major
Supporting
Additional
Algebra II – Polynomial Functions
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