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Subject: High School Mathematics
Unit Overview
Course: Algebra II
Unit: #1 Polynomials & Rational Expressions
Instructional Time: 3 Weeks
Essential Question(s)
1. What is a “zero” of a polynomial?
2. How can zeros of polynomials be interpreted?
3. How can coefficients for the Binomial Theorem be found?
4. What is the Fundamental Theorem of Algebra?
5. What is the connection between Rational Expressions and
Polynomials?
Big Idea(s)
If p(a) = 0 then (x – a ) is a factor of polynomial p(x).
The zeros of a polynomial are the x-intercepts of its graph.
Pascal’s Triangle can be used to easily find Binomial
Coefficients.
The number of possible complex zeros of a polynomial can
be determined by its degree.
Rational Expressions are formed with Polynomial
numerators and denominators.
© 2013 The K-12 Curriculum Project, Inc.
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Page 1
Unit Overview
Subject: High School Mathematics
Course: Algebra II
Unit: #1 Polynomials & Rational Expressions
Instructional Time: 3 Weeks
Priority Standards
A-APR2. 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-APR3. 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.
A-APR5. (+) 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.
A-APR6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + 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.
N-CN9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
© 2013 The K-12 Curriculum Project, Inc.
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Page 2
Unit Overview
Subject: High School Mathematics
Course: Algebra II
Unit: #1 Polynomials & Rational Expressions
Instructional Time: 3 Weeks
Priority
Standard
Connection
Supporting Standards
A-APR1. 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.
A-APR3
A-APR5
A-APR4. 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.
A-APR3
A-APR7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide
rational expressions.
A-APR6
N-CN8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
© 2013 The K-12 Curriculum Project, Inc.
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Page 3
A-APR3
N-CN9
Unit Overview
Subject: High School Mathematics
Course: Algebra II
Unit: #1 Polynomials & Rational Expressions
Instructional Time: 3 Weeks
Analysis of Priority Standards
A-APR2. 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).
Action
Bloom
Idea
DOK
Know
Knowledge
Polynomial, Remainder, Division of Polynomials
1
Apply
Application
P(a) = 0 if and only if (x-a) is a factor
3
A-APR3. 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.
Action
Bloom
Idea
DOK
Identify
Knowledge
Zeros of Polynomials
1
Use
Application
Construct a graph
2
n
A-APR5. (+) Know and apply the Binomial Theorem for the expansion of (x + y) 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.
Action
Bloom
Idea
DOK
n
Know
Knowledge
Binomial Theorem and expansion of (x + y)
1
Apply
Application
Coefficients determined by Pascal’s Triangle
3
A-APR6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + 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.
Action
Bloom
Idea
DOK
Rewrite
Synthesize
Different forms of rational expressions
2
Use
Application
Inspection, long division
2
N-CN9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Action
Bloom
Idea
DOK
Know
Knowledge
The Fundamental Theorem of Algebra
2
Show
Evaluation
Quadratic Polynomials
2
© 2013 The K-12 Curriculum Project, Inc.
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Page 4
Unit Overview
Subject: High School Mathematics
Course: Algebra II
Unit: #1 Polynomials & Rational Expressions
Instructional Time: 3 Weeks
© 2013 The K-12 Curriculum Project, Inc.
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Page 5