The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

Big Ideas Algebra 2 Chapter 4 focuses on the family of polynomial functions. Consult Algebra 2 Families of Functions for additional evidence outcomes that apply to polynomial functions.

HS.A-APR.B. Arithmetic with Polynomials & Rational Expressions: 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). (Students need not apply the Remainder Theorem to polynomials of degree greater than 4.) (CCSS: HS.A-APR.B.2)

• 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. (CCSS: HS.A-APR.B.3)

HS.F-IF.C. Interpreting Functions: Analyze functions using different representations. 

• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)

  • Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (CCSS: HS.F-IF.C.7.c)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Assessments:

• Chapter 4 Assessment (PDF)

• SAT Suite Educator Question Bank (Content Domain: Advanced Math)

• Additional Assessment Tasks

Instructional Resources & Notes:

• Big Ideas Algebra 2 Chapter 4 (skip Lessons 4.3, 4.6, 4.9)

• Supplemental Lesson Resources for Chapter 4

• Additional Modeling Tasks

  • Sweets for the Sweet, Box It Up, Global Smartphone Sales, National Park Attendance Trends, The Paths of the Planets (References: Completing the Modeling Cycle, Advice on Modeling)

• Notes: 

  • Students do not need to perform long division of polynomials or synthetic division in Chapter 4; Lesson 4.3 (Dividing Polynomials), including the Remainder Theorem, is optional and can be reserved for Honors Algebra 2 classes only.

  • Students do not need to know or use the Rational Root Theorem or the Irrational Conjugate Theorem to solve polynomial equations in Lesson 4.5; rather, students should solve polynomial equations by factoring and/or graphing. Be selective when choosing exercises for Lesson 4.5 (Solving Polynomial Equations).

  • In Lesson 4.8, use technology to graph polynomial functions. Focus on identifying local maximums, local minimums, and other key features of the graph by inspection. Be selective when choosing exercises for Lesson 4.8 (Analyzing Graphs of Polynomial Functions).