AII.1d 
The student, given rational, radical, or polynomial expressions, will
d) factor polynomials completely. 

Essential Knowledge and Skills 
 Factor polynomials by applying general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials.
 Factor polynomials completely over the integers.
 Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials. †Revised March 2011

Essential Understandings 
 The complete factorization of polynomials has occurred when each factor is a prime polynomial.
 Pattern recognition can be used to determine complete factorization of a polynomial.


Vertical Articulation 
 SOL A.1  represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables

Instructional Materials 
 VDOE ESS Lesson: Factoring  Expressions and Operations (PDF)  Factoring polynomials (Word)
 Notes: Factoring StepByStep Guide (ppt)
 Foldable: Factoring Techniques Outline (flipchart)
 Graphic: Factoring Flowchart (doc)

Real World Lessons 

Practice 
 VDOE ESS: Factor Patterns Worksheet (pdf)
 VDOE ESS: Factor, Factor, Factor! Worksheet (pdf)
 Worksheet: Factoring Binomials Practice (doc)
 Worksheet: Sum and Difference of Cubes (doc)
 Worksheet: Factoring Practice  Increased Rigor (doc)
 Journaling: Factoring Discussion Questions (doc)

SelfAssessments 
 SOL MiniQuiz: AII.1d  Factoring using Sum/Difference of Cubes

Skills 

Videos 

Explore
Learning 
 Factoring Special Products  Choose the correct steps to factor a polynomial involving perfectsquare binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps.
 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.
 Modeling the Factorization of ax^2+bx+c  Factor a polynomial with a leading coefficient greater than 1 using an area model. Use stepbystep feedback to diagnose any mistakes.

Websites 

Common Core
Standards 
ASSE.2 
AAPR.2 
AAPR.4 
AAPR.6 
AAPR.7 
FIF.8a 
