odpoveď:
Kvocient je # = X ^ 2 + x-3 # a zvyšok je # = 4x + 5 #
vysvetlenie:
Urobme dlhú divíziu
#COLOR (biely) (AAAA) ## X ^ 2 + 2x + 1 ##|##COLOR (biely) (aa) ## X ^ 4 + 3 ^ 3 + 0x ^ 2-x + 2 ##|##COLOR (biely) (aa) ## X ^ 2 + x-3 #
#COLOR (biely) (aaaaaaaaaaaaaaaaaa) ## X ^ 4 + 2x ^ 3 + x ^ 2 #
#COLOR (biely) (aaaaaaaaaaaaaaaaaaa) ## 0 + x ^ 3-x ^ 2-x #
#COLOR (biely) (aaaaaaaaaaaaaaaaaaaaa) ## + X ^ 3 + 2x ^ 2 + x #
#COLOR (biely) (aaaaaaaaaaaaaaaaaaaaaa) ## + 0-3x ^ 2-2x + 2 #
#COLOR (biely) (aaaaaaaaaaaaaaaaaaaaaaaaaa) ## -3x ^ 2-6x-3 #
#COLOR (biely) (aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa) ## 0 + 4x + 5 #
Kvocient je # = X ^ 2 + x-3 # a zvyšok je # = 4x + 5 #
# (X ^ 4 + 3 ^ 3x + 2) / (x ^ 2 + 2x + 1) = (x ^ 2 + x-3) + (4x + 5) / (x ^ 2 + 2x + 1) #
