Što je (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?

Što je (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?
Anonim

Odgovor:

Kvocijent je # = X ^ 2 + x-3 # a ostatak je # = 4x + 5 #

Obrazloženje:

Provedimo dugu podjelu

#COLOR (bijeli) (aaaa) ## 2 x ^ + 2x + 1 ##|##COLOR (bijeli) (aa) ## X ^ 4 ^ 3 + 3x + 0x ^ 2-x + 2 ##|##COLOR (bijeli) (aa) ## 2 x ^ + x-3 #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaa) ## X ^ 4 + 2x ^ 3 + x ^ 2 #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaaa) ## 0 + x ^ 3 ^ 2 x-x #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaaaaa) ## + X ^ 3 + 2 + 2x ^ x #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaaaaaa) ## + 0-3x ^ 2-2x + 2 #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaaaaaaaaaa) ## -3x ^ 2-6x-3 #

#COLOR (bijeli) (aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa) ## 0 + 4x + 5 #

Kvocijent je # = X ^ 2 + x-3 # a ostatak je # = 4x + 5 #

# (X ^ 4 ^ + 3x 3x + 2) / (x ^ 2 + 2x + 1) = (x ^ 2 + x-3) + (4x + 5) / (x ^ 2 + 2x + 1) #