Scribd
Upload
63 views2 pages

3.6 Factoring Polynomials PDF

The document discusses the remainder theorem and factor theorem for polynomials. It provides examples of using these theorems to factor polynomials and determine if expressions are factors. It also gives examples of using the theorems to find the remainder of a polynomial division and determine coefficients.

Uploaded by

Ashley Elliott
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
63 views2 pages

3.6 Factoring Polynomials PDF

The document discusses the remainder theorem and factor theorem for polynomials. It provides examples of using these theorems to factor polynomials and determine if expressions are factors. It also gives examples of using the theorems to find the remainder of a polynomial division and determine coefficients.

Uploaded by

Ashley Elliott
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

MHF4U1 Unit 2 Lesson 6

Factoring  3.6  
Learning  goal  
•   Know  the  remainder  theorem  
•   Know  the  factor  theorem.    Be  able  to  use  the  factor  theorem  to  factor  a  polyomial  of  
degree  3  or  higher  
 
Remainder  Theorem  
When  a  polynomial  function  P(x)  is  divided  by  binomial  (x-­‐‑a),  the  remainder  is  equal  to  f(a).    If  
the  remainder  is  0,  then  x-­‐‑a    is  a  factor  of  the  polynomial.      
 
Factor  theorem  
x-­‐‑a  is  a  factor  of  f(x)  if  and  only  if  f(a)  =  0  
 
Example  1  Determine  the  remainder  given  𝑓 (𝑥 ) = 2𝑥 ' − 4𝑥 * + 3𝑥 − 6      divided  by  (x+2)  
 
 
 
 
 
 
Example  2  Confirm  that  (x+4)  is  a  factor  of  the  polynomial  function  𝑓 (𝑥 ) =  2𝑥 ' + 𝑥 * − 43𝑥 −
60.          Then  completely  factor  the  polynomial  and  sketch  the  function  
 
 
 
 
 
 
 
 
 
 
 
 

1
MHF4U1 Unit 2 Lesson 6
Example  3–  Determine  a  factor  of  the  function  𝑓(𝑥 ) =  3𝑥 1 − 23𝑥 ' + 7𝑥 * + 155𝑥 + 50    .    
Completely  factor  the  function,  and  sketch  the  function.  
 
 
 
 
 
 
 
 
 
 
 
Example  4  –  The  function  𝑓(𝑥 ) =  3𝑥 ' + 𝑚𝑥 * − 41𝑥 + 𝑛        has  a  factor  of  (x-­‐‑3).    When  it  is  
divided  by  (x+2)  the  remainder  is  95.    Use  the  remainder  theorem  and  the  factor theorem to
determine the  values  of  m  and  n.  

You might also like