Hvad er kvotienten af d ^ 4 - 6d ^ 3 + d + 17 med d-2?

Svar:

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

Udfør en lang division for at opnå kvotienten

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

#COLOR (hvid) (aaaa) ## D ^ 4-2d ^ 3 ##COLOR (hvid) (aaaaaaaaaaaaaaaaa) ##|## D ^ 3-4d ^ 2-8d-15 #

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

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

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

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

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

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

#COLOR (hvid) (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) #