Schemat Hornera
a)
[tex]\begin{array}{c||c|c|c|c}&1&-6&12&-8\\2&1&-4&4&0\end{array}\\\\\cfrac{x^3-6x^2+12x-8}{x-2}=x^2-4x+4\ ,\ x\not=2[/tex]
b)
[tex]\begin{array}{c||c|c|c|c|c}&1&1&1&4&3\\-1&1&0&1&3&0\end{array}\\\\\cfrac{x^4+x^3+x^2+4x+3}{x+1}=x^3+x+3\ ,\ x\not=-1[/tex]
c)
[tex]\begin{array}{c||c|c|c|c|c}&2&-8&0&5&-20\\4&2&0&0&5&0\end{array}\\\\\cfrac{2x^4-8x^3+5x-20}{x-4}=2x^3+5\ ,\ x\not=4[/tex]
Mnożenie pisemne
a)
[tex]\ \ \ (x^3-6x^2+12x-8):(x-2)=x^2-4x-4\ ,\ x\not=2\\\cfrac{-x^3+2x^2\ \ \ \ \ \ \ \ }{\ \ \ \ \ \ \ -4x^2+12x}\\\cfrac{\ \ \ \ \ -4x^2-8x\ \ \ }{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -4x-8}\\\cfrac{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4x+8}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0}[/tex]
b)
[tex]\ \ \ (x^4+x^3+x^2+4x+3):(x+1)=x^3+x+3\ ,\ x\not=-1\\\cfrac{-x^4-x^3\ \ \ \ \ \ \ \ \ \ \ \ \ }{\ \ \ \ \ \ \ \ \ \ \ 0+x^2+4x}\\\cfrac{\ \ \ \ \ \ \ \ \ -x^2-x\ \ \ }{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x+3}\\\cfrac{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -3x-3}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0}[/tex]
c)
[tex]\ \ \ (2x^4-8x^3+5x-20):(x-4)=2x^3+5\ ,\ x\not=4\\\cfrac{-2x^4+8x^3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }{\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0+5x-20}\\\cfrac{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -5x+20\ \ \ }{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0}[/tex]
