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58 | eUreka Math algebra II StUdy gUIde
Module 1: Polynomial, Rational, and Radical Relationships
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In this module, students draw on their foundation of the analogies between polynomial
arithmetic and base-10 computation, focusing on properties of operations, particularly the
distributive property (A-SSE.B.2, A-APR.A.1). Students connect multiplication of polynomials
with multiplication of multi-digit integers and division of polynomials with long division of
integers (A-APR.A.1, A-APR.D.6). Students identify zeros of polynomials, including complex zeros
of quadratic polynomials, and make connections between zeros of polynomials and solutions of
polynomial equations (A-APR.B.3). Students explore the role of factoring, as both an aid to the
algebra and to the graphing of polynomials (A-SSE.2, A-APR.B.2, A-APR.B.3, F-IF.C.7c). Students
continue to build on the reasoning process of solving equations as they solve polynomial,
rational, and radical equations, as well as linear and nonlinear systems of equations (A-REI.A.1,
A-REI.A.2, A-REI.C.6, A-REI.C.7). The module culminates with the fundamental theorem of
algebra as the ultimate result in factoring. Students pursue connections to applications in
prime numbers in encryption theory, Pythagorean triples, and modeling problems.
An additional theme of this module is that the arithmetic of rational expressions is
governed by the same rules as the arithmetic of rational numbers. Students use appropriate
tools to analyze the key features of a graph or table of a polynomial function and relate those
features back to the two quantities that the function is modeling in the problem (F-IF.C.7c).
The module comprises 40 lessons; 5 days are reserved for administering the Mid- and
End-of-Module Assessments, returning the assessments, and remediating or providing
further applications of the concepts. The Mid-Module Assessment follows Topic B.
The End-of-Module Assessment follows Topic D.
Focus standaRds
Reason quantitatively and use units to solve problems.
N-Q.A.2^1 Define appropriate quantities for the purpose of descriptive modeling.★
Perform arithmetic operations with complex numbers.
N-CN.A.1 Know there is a complex number i such that i^2 =- 1 , and every complex number
has the form ab+ i with a and b real.
N-CN.A.2 Use the relation i^2 =-^1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Use complex numbers in polynomial identities and equations.
N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
Interpret the structure of expressions.
A-SSE.A.2^2 Use the structure of an expression to identify ways to rewrite it. For example,
see xy^44 - as ()xy^22 - ()^22 , thus recognizing it as a difference of squares that can be factored
as ()xy^22 -+()xy^22.