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)
 Notes: Factoring Using Difference of Squares (doc)  Teacher Key (pdf)
 Activity: Illuminations  Factoring with Algetiles  select Factor tab

Real World Lessons 

Practice 
 Worksheet: Factoring Using Difference of Squares Classwork (doc)
 Worksheet: Factoring Using Difference of Squares Homework (doc)
 ExamView Quiz: Factoring Difference of Squares

SelfAssessments 

Skills 

Videos 
 Video: PH Factoring Difference of Squares

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.

Websites 
 Interactive Notes: Factoring  lessons and practice problems from Regentsprep.org
 Interactive Notes: Square Roots Review  notes and workout problems from Math.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 
