Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
A.2c
The student will perform operations on polynomials, including
c)   factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.

Essential Knowledge and Skills 
  • Factor completely first- and second-degree polynomials with integral coefficients.
  • Identify prime polynomials.
  • Use the x-intercepts from the graphical representation of the polynomial to determine and confirm its factors.
Essential Understandings
  • Factoring reverses polynomial multiplication.
  • Some polynomials are prime polynomials and cannot be factored over the set of real numbers.
  • Polynomial expressions can be used to define functions and these functions can be represented graphically.
  • There is a relationship between the factors of any polynomial and the x-intercepts of the graph of its related function.
Vertical Articulation
  1. SOL 7.16 - apply properties w/ real numbers: a) commutative and associative properties for add/multi; b) distributive property; c) add/multi identity properties; d) add/multi inverse properties; e) multi property of zero
  2. SOL 8.15 - c) identify properties of operations used to solve equations
  3. SOL AII.3 - perform operations on complex numbers/express results in simplest form using patterns of the powers of i, identify field properties for complex numbers
Instructional Materials
  1. VDOE ESS Lesson: Factoring - Expressions and Operations (PDF) - Factoring polynomials (Word)
  2. Modeling: Factoring Trinomials with Algebra Tiles (ppt)
  3. Notes: Factoring Trinomials by Grouping (ppt)
  4. Notes: Factoring Trinomials by Trial and Error (ppt)
  5. Notes: Factoring 4 terms by Grouping (ppt)
  6. Notes: Factoring Trinomials (doc) | Teacher Key (doc)
  7. Activity: Illuminations - Factoring with Algetiles - select Factor tab
Real World Lessons
Practice
  1. VDOE ESS: Squares Factoring Puzzle (pdf)
  2. Worksheet: Factoring Trinomials Classwork (doc)
  3. Worksheet: Factoring Trinomials Homework (doc)
  4. ExamView Quiz: Factoring Trinomials
  5. Prentice Hall Quiz: Factoring Trinomials (a=1)
  6. Prentice Hall Quiz: Factoring Trinomials (a≠1)
  7. Prentice Hall Quiz: Factoring by Grouping
  8. ExamView Quiz: Factoring Perfect Square Trinomials
  9. Prentice Hall Quiz: Factoring Special Trinomials
Self-Assessments
Skills
  1. Mathematics Assessment Project
    • A06:Sidewalk Patterns - Apprentice - In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes. In this task, you will look for rules which let you work out how many blocks of different colors are needed to make different sized patterns. (This task is very similar to Sidewalk Stones, but offers more step-by-step guidance.)
    • E13:Sidewalk Stones - Expert - This task is very similar to Sidewalk Patterns, but offers less step-by-step guidance.
  2. JMU PIvotal Question: Factoring Trinomials (doc)
Videos
  1. Factoring Trinomials with Leading Coefficient of 1
    1. PH Factoring Trinomials of the Type x^2 + bx + c (where b is positive)
    2. PH Factoring Trinomials of the Type x^2 - bx + c (where b is negative)
    3. PH Factoring Trinomials of the Type x^2 + bx – c (where c is negative)
    4. PH Factoring Perfect Square Trinomials
  2. Factoring Trinomials with Leading Coefficient not equal (≠) to 1
    1. PH Factoring Trinomials of the Type ax^2 + bx + c (where c is positive)
    2. PH Factoring Trinomials of the Type ax^2 + bx - c (where c is negative)
    3. Factoring perfect square trinomials with a ≠ 1
  3. Factoring by Grouping
    1. Factoring a four-term Polynomial by Grouping
    2. Factoring Trinomials by Grouping
  4. PH Factoring Perfect Square Trinomials with a = 1
  5. PH Factoring perfect square trinomials with a ≠ 1
  6. PH Factoring Trinomials with Two Variables
  7. PH Real World Factoring Problems
Explore Learning
  1. Modeling the Factorization of x^2+bx+c - Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step‑by‑step feedback to diagnose any mistakes.
  2. Quadratics in Factored Form: Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
Websites
  1. Interactive Notes: Factoring - lessons and practice problems from Regentsprep.org
  2. Notes: Factoring Quadratics - notes on factoring trinomials at Purplemath.com
Old Website Links
Common Core Standards
7.EE.1
8.EE.1
N-RN.1
N-RN.2
A-SSE.2
A-SSE.3a
A-SSE.3b
A-SSE.3c
A-APR.1
A-APR.4
F-IF.8a