Ano ang (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?

Ano ang (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?
Anonim

Sagot:

Ang kusyente ay # = x ^ 2 + x-3 # at ang natitira ay # = 4x + 5 #

Paliwanag:

Magsagawa tayo ng mahabang dibisyon

#color (white) (aaaa) ## x ^ 2 + 2x + 1 ##|##color (white) (aa) ## x ^ 4 + 3x ^ 3 + 0x ^ 2-x + 2 ##|##color (white) (aa) ## x ^ 2 + x-3 #

#color (white) (aaaaaaaaaaaaaaaaaa) ## x ^ 4 + 2x ^ 3 + x ^ 2 #

#color (white) (aaaaaaaaaaaaaaaaaaa) ## 0 + x ^ 3-x ^ 2-x #

#color (white) (aaaaaaaaaaaaaaaaaaaaa) ## + x ^ 3 + 2x ^ 2 + x #

#color (white) (aaaaaaaaaaaaaaaaaaaaaa) ## + 0-3x ^ 2-2x + 2 #

#color (white) (aaaaaaaaaaaaaaaaaaaaaaaaaa) ## -3x ^ 2-6x-3 #

#color (white) (aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa) ## 0 + 4x + 5 #

Ang kusyente ay # = x ^ 2 + x-3 # at ang natitira ay # = 4x + 5 #

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