Çözüldü Polinomlarda Bölünme ve Belirsiz Katsayılar Kuralı

https://i72.servimg.com/u/f72/19/97/10/39/polino43.png
https://www.facebook.com/photo?fbid=10233843399279493&set=pcb.2530906133954551

P(x) = (x^2 + x + 1)·Q(x) + a·x + b
P(x) - a·x - b = (x^2 + x + 1)·Q(x)
(x - 1)[ P(x) - a·x - b ] = (x^3 - 1)·Q(x)
(x - 1)(x^59 - 3x^42 + 4x - 2 - a·x - b) = (x^3 - 1)·Q(x)
(x - 1)[ x^59 - 3x^42 + (4 - a)x - (2 + b) ] = (x^3 - 1)·Q(x)
x^60 - 3x^43 + (4 - a)·x^2 - (2 + b)x - x^59 + 3x^42 + (a - 4)x + (b + 2) = (x^3 - 1)·Q(x)
x^60 - x^59 - 3x^43 + 3x^42 + (4 - a)·x^2 + (a - 4 - 2 - b)x + (b + 2) = (x^3 - 1)·Q(x)
(x^3)^20 - (x^3)^19·x^2 - 3(x^3)^14·x + 3(x^3)^14 + (4 - a)·x^2 + (a - b - 6)x + (b + 2) = (x^3 - 1)·Q(x)
1^20 - 1^19·x^2 - 3·1^14·x + 3·1^14 + (4 - a)·x^2 + (a - b - 6)x + (b + 2) = (1 - 1)·Q(x)
1 - x^2 - 3x + 3 + (4 - a)·x^2 + (a - b - 6)x + (b + 2) = 0
(4 - a - 1)·x^2 + (a - b - 6 - 3)x + b + 6 = 0
(3 - a)·x^2 + (a - b - 9)x + b + 6 = 0
3 - a = 0 ⇒ a = 3
3 - b - 9 = 0 ⇒ b = -6
Kalan = 3x - 6.

WolframAlpha Kontrolu:

https://i72.servimg.com/u/f72/19/97/10/39/polino44.png
https://www.wolframalpha.com/input?i=quotient and remainder (x^59-3x^42 + 4x - 2)/(x^2+x+1)