
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 10th, 2012, 09:28 AM  #1 
Newbie Joined: Sep 2012 Posts: 8 Thanks: 0  Find f(x) from the following information
Let f(x) be a polynomial of degree less than or equal to 5 which leaves remainders 1 and 1 respectively upon division by and . Find f(x).

October 10th, 2012, 04:23 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,593 Thanks: 1491 
f(x) = (3x^5 + 10x^3  15x)/8

October 10th, 2012, 05:00 PM  #3  
Newbie Joined: Oct 2012 Posts: 1 Thanks: 0  Quote:
 
October 10th, 2012, 06:38 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,593 Thanks: 1491 
If you meant the divisor to be (x + 2) rather than just x, see the division below. x^2 + 3x  1 _________________ x + 2  x^3 + 5x^2 + 5x + 19 x^3 + 2x^2  3x^2 + 5x 3x^2 + 6x  x + 19 x  2  21 
October 11th, 2012, 05:51 AM  #5  
Newbie Joined: Sep 2012 Posts: 8 Thanks: 0  Re: Quote:
 
October 11th, 2012, 05:58 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,593 Thanks: 1491 
I couldn't spot any simple method, so I wrote f(x) = (ax² + bx + c)(x  1)³  1 = (px² + qx + r)(x + 1)³ + 1. On expanding and equating coefficients, one has six equations for the six coefficients of the quadratics. Solving these equations allows f(x) to be found.

October 11th, 2012, 06:14 AM  #7  
Newbie Joined: Sep 2012 Posts: 8 Thanks: 0  Quote:
 
October 11th, 2012, 06:27 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,593 Thanks: 1491 
In general, the remainder on dividing a function f(x) by (x  a)^n would be a nonconstant function of x. If that function is R(x), you would know that R(a) = f(a).


Tags 
find, information 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Need Information ..  nagrajkundan  Academic Guidance  0  December 2nd, 2011 08:44 AM 
questions about fisher information  almond321  Advanced Statistics  0  July 25th, 2011 08:53 PM 
Storing area information  sisx  Algebra  0  February 23rd, 2010 08:59 AM 
Entropy (information theory)  trid2  Advanced Statistics  1  March 1st, 2009 07:24 PM 
information abt legendar.....  esraamajed  Number Theory  2  March 27th, 2008 09:52 AM 