Download Unit5Algebra2(chapter 6)

Hempfield School District Curriculum: Unit Template
Course Title: Algebra II
Unit Title: Polynomials and Polynomial Functions
Names of Teachers who Developed Unit:
Dates Developed:
Approximate Dates when Taught During School Year:
Approximate Number of Periods:
Summary:
Print Materials Needed:
Resources:
Internet Resource Links:
Stage 1: Desired Results
Essential Questions (Include PA Standards, Anchors & Eligible Content)
Big Ideas:
• Relations and functions are mathematical relationships that can be represented and
analyzed using words, tables, graphs, and equations.
• Families of functions exhibit properties and behaviors that can be recognized across
representations. Functions can be transformed, combined, and composed to create new
functions in mathematical and real world situations.
• Bivariate data can be modeled with mathematical functions that approximate the data well
and help us make predictions based on the data.
• There are some mathematical relationships that are always true and these relationships
are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of
expressions and solving equations and inequalities.
• Probability expresses the likelihood that a particular event will occur. Mathematical
properties can be used to determine a theoretical probability. Various counting methods can
be used to develop theoretical probabilities.
Essential Questions:
• How do you identify and classify a polynomial function?
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Hempfield School District Curriculum: Unit Template
• How are the zeros of the polynomial function, the factors of the polynomial, and the
solutions to the polynomial related?
• How can synthetic division or long division of polynomials help graph or factor
polynomials?
• How do you solve polynomial equations?
• What is the difference between a permutation and a combination?
Assessment Anchors:

Eligible Content:

Know
Understand
Do
Vocabulary:
Students will understand: The Students will be Able to:
Polynomial
• A polynomial function
• Identify a polynomial.
Polynomial function
can be written in the
Degree
form
• Classify a polynomial by degree and
p(x)  an x n  an 1 x n 1  ... a1number
x  a0 of terms.
Standard form of a
polynomial
where n is a
Degree of a polynomial nonnegative integer and • Find a polynomial function that
Relative maximum
models real-world data and use it to
the coefficients an ,...,a0

Relative minimum
make predictions.
are real numbers.
Factor Theorem
Multiple zero
• Write a polynomial in standard form.
• A polynomial can be

Multiplicity
classified by its degree
Synthetic division
and/or number of terms. • Write a polynomial in factored form.
Remainder Theorem
Sum of cubes
• The x-intercepts of the • Find the zeros of a polynomial
Difference of cubes
function.
graph of a function are
Rational Root Theorem
called zeros because the
Conjugates
value of the function is 0 • Write a polynomial function form its
Irrational Root Theorem at each x-intercept.
zeros.
Complex conjugates
Imaginary Root
• Find the multiplicity of a zero.
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Hempfield School District Curriculum: Unit Template
Theorem
Fundamental Theorem
of Algebra
Permutation
N factorial
Combination

• The expression x  a is
a factor of a polynomial
• Divide a polynomial by a binomial
if and only if the value a using long division.
is a zero of the related

polynomial.
• Determine if a binomial is a factor of
a trinomial.

• If a is a zero of a
given polynomial then a • Divide a polynomial by a binomial
is a solution or root of
using synthetic division.
the equation.
• Evaluate a polynomial using synthetic

• Polynomial long
division and the Remainder Theorem.
division or synthetic
division can be used to
• Solve a polynomial equation by
find the factors of a
graphing.
polynomial. If the
remainder is zero, the
• Solve polynomial equations by
binomial is a factor of
factoring and using the Zero Product
the polynomial.
Property.
• If a polynomial is in
factored form, you can
use the zero product
property to find the
zeros of the function or
solutions of the
equation.
• You can graph each
side of a polynomial
equation and find the x values at the point(s) of
intersection. This
method will only

produce real number
solutions.
• The Rational Root
Theorem, the Irrational
Root Theorem, and the
Imaginary Root
Theorem can help find
possible roots of a
polynomial equation.
• Factor a sum or difference of cubes.
• Use the Rational Root Theorem to
find a list of all the possible rational
roots of a polynomial function
• Find irrational and imaginary roots
using conjugates or complex
conjugates.
• Write a polynomial equation from its
roots.
• For a given polynomial equation, find
the number of complex roots and the
possible number of real roots.
• Find all of the complex zeros of a
polynomial function.
• Use the factorial function.
• Find permutations.
• Find combinations.
• Including complex and
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Hempfield School District Curriculum: Unit Template
multiple roots, an nth
degree polynomial
equation has exactly n
roots and the related

polynomial function has
exactly n zeros.

• Solve real-world problems using
permutations and combinations.
• A permutation is an
arrangement of items in

which order matters. A
combination is a
selection of items that in
which order does not
matter.
Stage 2: Assessment Evidence
Assessments/Performance Tasks
Rubric Titles
Benchmark(s) for Course: Unit’s key Assessments
Self-Assessments
Other Evidence, Summarized
Stage 3: Learning Activities
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Hempfield School District Curriculum: Unit Template
Differentiation:
Readiness

.
Profile: Learning Styles /
Multiple Intelligences

Interest

Accommodations for ELLs:

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