Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
AII.8
The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
Essential Knowledge and Skills 
  • Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
  • Define a polynomial function, given its zeros.
  • Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function.
  • For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function.
  • Given a polynomial equation, determine the number of real solutions and nonreal solutions.
Essential Understandings
  • The Fundamental Theorem of Algebra states that, including complex and repeated solutions, an nth degree polynomial equation has exactly n roots (solutions).
  • The following statements are equivalent:
    • k is a zero of the polynomial function  f;
    • (xk) is a factor of  f(x);
    • k is a solution of the polynomial equation f(x) = 0; and
    • k is an x-intercept for the graph of  y = f(x).
Vertical Articulation
  1. SOL A.2 - perform operations on polynomials ‐ c) factor first and second degree binomials/trinomials (1 or 2 variables)
Instructional Materials
  1. VDOE ESS Lesson: Factors, Zeros, and Solutions - Functions (PDF) - Exploring relationships among factors, zeros, and solutions (Word)
  2. Notes: Quadratics - Connecting the Dots (ppt)
  3. Activity: Making Connections (zip)
Real World Lessons
Practice
  1. VDOE ESS: Zeros and Factors Worksheet (pdf)
  2. Worksheet: Connections Between Graphs and Factors (doc)
Self-Assessments
  1. SOL Mini-Quiz: AII.8 - Solutions, Zeros, and Factors
Skills
  1. Mathematics Assessment Project: A17:Cubic Graph - Apprentice - In this task, you will look at the properties of a cubic equation.
  2. JMU Pivotal Question: Relationships Among Zeros, Intercepts, Factors, and Solutions (doc)
Videos
Explore Learning
  1. Polynomials and Linear Factors - Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.
Websites
Common Core Standards
N-CN.9
A-APR.3