Hva er kvoten av d ^ 4 - 6d ^ 3 + d + 17 med d-2?

Svar:

Kvoten er # = D ^ 3-4d 2-8d ^ 15 #-

Utfør en lang divisjon for å skaffe kvotienten

#COLOR (hvit) (AAAA) ## D ^ 4-6d ^ 3 + 0d ^ 2 + d + 17 ##COLOR (hvit) (AAAA) ##|## D-2 #

#COLOR (hvit) (AAAA) ## D ^ 4-2d ^ 3 ##COLOR (hvit) (aaaaaaaaaaaaaaaaa) ##|## D ^ 3-4d 2-8d ^ 15 #-

#COLOR (hvit) (aaaaa) ## 0-4d ^ 3 + 0d ^ 2 #

#COLOR (hvit) (aaaaaaa) ## -4d ^ 3 + 8d ^ 2 #

#COLOR (hvit) (aaaaaaaa) ## -0-8d ^ 2 + d #

#COLOR (hvit) (aaaaaaaaaaaa) ## -8d ^ 2 + 16d #

#COLOR (hvit) (aaaaaaaaaaaaaa) ## -0-15d + 17 #

#COLOR (hvit) (aaaaaaaaaaaaaaaaaa) ## -15d + 30 #

#COLOR (hvit) (aaaaaaaaaaaaaaaaaaaa) ##-0-13#

Kvoten er # = D ^ 3-4d 2-8d ^ 15 #-

Resten er #=-13#

# (D ^ 4-6d ^ 3 + 0d ^ 2 + d + 17) / (d-2) = d ^ 3-4d 2-8d ^ 15-13-/ (d-2) #