Polynomial 
Functions   







 Topic  Mastery Objectives

Student should be able to...
 Videos  Survey IXL Practice  Answer Keys
   

   Classifying and Simplifying
   Polynomial Expressions



   Graphing Polynomial Functions

 
classify a polynomial by degree and number of terms.


simplify a polynomial and write it in standard form.


add, subtract and multiply polynomials.


sketch a polynomial function with the correct zeros & end behavior.

write an equation of a polynomial function from a table or graph given its zeros. 

 



http://www.youtube.com/watch?v=rQ7F1md4rKA&feature=youtu.be

 





 

Add/Sub

Graph Matching

 




     Polynomial Modeling

           LaGrange Interpolation
     
 


write a polynomial equation for any set of given points (ordered pairs).
  
       
  

 



   

     

   
     
Linear Regression

use the graphing calculator to determine a polynomial regression model for a data set.

use a regression model to predict within the data set.


 https://www.youtube.com/watch?v=cENgV1trBgo&feature=youtu.be
   
      https://dl.dropboxusercontent.com/u/17556721/Systems%20Videos/KEYS/Linear%20Regression.pdf
   
     Dividing Polynomials 

            Long Division



            Synthetic Division

 

divide polynomials using long division.


divide polynomials using synthetic division (when possible).


determine if a polynomial is a factor of another polynomial.


solve polynomial equations given one of its solutions.

determine the remainder when any polynomial is divided by a linear polynomial.
 


 
http://www.youtube.com/watch?v=lcKFLhiRrco
 

Why synthetic division works?
 





 









 

     

 
     
  
    Quiz Review


       

   Factoring by Grouping



factor polynomials by grouping if possible.

factor the sum and difference of cubes.

      
http://www.youtube.com/watch?v=psfWd-4a0gQ
 
 
 
 
     
 

   Binomial Theorem


 
use the binomial theorem expand a binomial expression raised to a positive integer power.

identify terms of a binomial expansion without determining the entire expansion.


 http://www.youtube.com/watch?v=RaxM9ljaesk
 
https://docs.google.com/forms/d/1_N3YEb33BCMNrbJ4Lld7vKEM6GI9tLlSOoAq-DyPQk0/viewform

 





   Fundamental Theorem of Algebra

   Rational Root Theorem



identify the number of complex roots of any polynomial equation.

identify the possible rational roots of any polynomial equation.

determine all rational roots of any polynomial equation.
 
 

http://www.youtube.com/watch?v=qmjqVL_5A2g&feature=youtu.be
 
 




 
Fundamental Theorem of Algebra

https://www.ixl.com/math/algebra-2/rational-root-theorem
Rational Root Theorem

 



  
   Irrational Root Theorem

   Non-Real Root Theorem

 
identify the congujate roots of a polynomial equation when applicable.

recognize that any polynomial equation with non-real roots must have an even number of non-real roots.
 
http://www.youtube.com/watch?v=p0EVyjyyP-g

 

 
Conjugate Root Theorems

 
  
    Applications


determine a polynomial model for a contextualized problem (ex/ volume).

use a graphing calculator to identify extrema, zeros or other significant values when a "real-life situation" can be modeled by a polynomial function.

    

  
    Test Review