Svar:
Kvoten er # = (D ^ 3-4d ^ 2-8d-15) #
Forklaring:
Lad os udføre den lange division
# D-2 ##COLOR (hvid) (aaaa) ##|## D ^ 4-6d ^ 3 + 0d ^ 2 + d + 17 ##COLOR (hvid) (aa) ##|## D ^ 3-4d ^ 2-8d-15 #
#COLOR (hvid) (aaaaaaaaaa) ## D ^ 4-2d ^ 3 #
#COLOR (hvid) (aaaaaaaaaaa) ## 0-4d ^ 3 + 0d ^ 2 #
#COLOR (hvid) (aaaaaaaaaaaaa) ## -4d ^ 3 + 8 D ^ 2 #
#COLOR (hvid) (aaaaaaaaaaaaaa) ## -0-8d ^ 2 + d #
#COLOR (hvid) (aaaaaaaaaaaaaaaaa) ## -8d ^ 2 + 16d #
#COLOR (hvid) (aaaaaaaaaaaaaaaaaaa) ## -0-15d + 17 #
#COLOR (hvid) (aaaaaaaaaaaaaaaaaaaaaaa) ## -15d + 30 #
#COLOR (hvid) (aaaaaaaaaaaaaaaaaaaaaaaaa) ##-0-13#
Derfor, # (D ^ 4-6d ^ 3 + d + 17) / (d-2) = d ^ 3-4d ^ 2-8d-15-13 / (d-2) #
Resten er #=-13# og kvotienten er # = (D ^ 3-4d ^ 2-8d-15) #
