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December 2nd, 2016, 07:05 AM  #1 
Senior Member Joined: Feb 2014 Posts: 114 Thanks: 1  Polynomial function transform two function
Hello, I have polynomial function (Blue function) and write this to two independent function. Now red function is F(x) based F0(x) and F1(x). How can write red function? Thanks 
December 2nd, 2016, 07:39 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Is that first thing written in f(x) a 4? That is, is $\displaystyle f(x)= 4+ 3x+ 5x^2+ 7x^3+ 2x^4+ 5x^5$? Which you then separate into "even" and "odd" powers $\displaystyle = (4+ 5x^2+ 2x^4)+ (3x+ 7x^3+ 5x^5)$ and factor "x" out of the odd powers $\displaystyle = (4+ 5x^2+ 2x^4)+ x(3+ 7x^2+ 5x^4)$ You then also have defined $\displaystyle f_0(x)= 4+ 5x^2+ 2x^4$ and $\displaystyle f_1(x)= 3+ 7x^2+ 5x^4$. Then, yes, the function above is $\displaystyle f(x)= f_0(x)+ xf_1(x)$ (It is not a good idea to use "x" as a variable and also as a multiplication sign which you appear to have done! Use "*" if not just "juxtaposition" to indicate multiplication.) 
December 2nd, 2016, 08:29 AM  #3 
Senior Member Joined: Feb 2014 Posts: 114 Thanks: 1 
Exactly but we have power 2 I problem with this. I rewrite the red function. Last edited by life24; December 2nd, 2016 at 08:32 AM. 

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