A.2c 
The student will perform operations on polynomials, including
c) factoring completely first and seconddegree 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 seconddegree polynomials with integral coefficients.
 Identify prime polynomials.
 Use the xintercepts 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 xintercepts of the graph of its related function.


Vertical Articulation 
 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
 SOL 8.15  c) identify properties of operations used to solve equations
 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 
 VDOE ESS Lesson: Factoring  Expressions and Operations (PDF)  Factoring polynomials (Word)
 Modeling: Factoring Trinomials with Algebra Tiles (ppt)
 Notes: Factoring Trinomials by Grouping (ppt)
 Notes: Factoring Trinomials by Trial and Error (ppt)
 Notes: Factoring 4 terms by Grouping (ppt)
 Notes: Factoring Trinomials (doc)  Teacher Key (doc)
 Activity: Illuminations  Factoring with Algetiles  select Factor tab

Real World Lessons 

Practice 
 VDOE ESS: Squares Factoring Puzzle (pdf)
 Worksheet: Factoring Trinomials Classwork (doc)
 Worksheet: Factoring Trinomials Homework (doc)
 ExamView Quiz: Factoring Trinomials
 Prentice Hall Quiz: Factoring Trinomials (a=1)
 Prentice Hall Quiz: Factoring Trinomials (a≠1)
 Prentice Hall Quiz: Factoring by Grouping
 ExamView Quiz: Factoring Perfect Square Trinomials
 Prentice Hall Quiz: Factoring Special Trinomials

SelfAssessments 

Skills 
 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 stepbystep guidance.)
 E13:Sidewalk Stones  Expert  This task is very similar to Sidewalk Patterns, but offers less stepbystep guidance.
 JMU PIvotal Question: Factoring Trinomials (doc)

Videos 
 Factoring Trinomials with Leading Coefficient of 1
 PH Factoring Trinomials of the Type x^2 + bx + c (where b is positive)
 PH Factoring Trinomials of the Type x^2  bx + c (where b is negative)
 PH Factoring Trinomials of the Type x^2 + bx – c (where c is negative)
 PH Factoring Perfect Square Trinomials
 Factoring Trinomials with Leading Coefficient not equal (≠) to 1
 PH Factoring Trinomials of the Type ax^2 + bx + c (where c is positive)
 PH Factoring Trinomials of the Type ax^2 + bx  c (where c is negative)
 Factoring perfect square trinomials with a ≠ 1
 Factoring by Grouping
 Factoring a fourterm Polynomial by Grouping
 Factoring Trinomials by Grouping
 PH Factoring Perfect Square Trinomials with a = 1
 PH Factoring perfect square trinomials with a ≠ 1
 PH Factoring Trinomials with Two Variables
 PH Real World Factoring Problems

Explore
Learning 
 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.
 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 
 Interactive Notes: Factoring  lessons and practice problems from Regentsprep.org
 Notes: Factoring Quadratics  notes on factoring trinomials at Purplemath.com

Old Website Links 

Common Core
Standards 
7.EE.1 
8.EE.1 
NRN.1 
NRN.2 
ASSE.2 
ASSE.3a 
ASSE.3b 
ASSE.3c 
AAPR.1 
AAPR.4 
FIF.8a 
