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p(x) bir polinom olmak üzere, P(x)+p(x kare) = 2x kare +2x -4 ise p(x) in 2x+1 ile bölümünden kalan nedir?

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[tex]P(x)=ax+b \\P(x^{2})=ax^{2}+b \\P(x)+P(x^{2})=2x^{2}+2x-4 \\ax+b+ax^{2}+b=2x^{2}+2x-4 \\ax^{2}+ax+2b=2x^{2}+2x-4 \\ax^{2}=2x^{2} ise ...a=2 \\2b=-4ise...b=-2[/tex]

 

P(x)=2x-2  olarak bulunur 2x+1'e bölümünü soruyor [tex]x=-\frac{1}{2}[/tex] alırsak;

 

[tex]P(-\frac{1}{2})=2.(-\frac{1}{2})-2 \\P(-\frac{1}{2})=-1-2 \\P(-\frac{1}{2})=-3[/tex] olarak bulunur

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