(x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)은 무엇입니까?

(x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)은 무엇입니까?
Anonim

대답:

몫은 # = x ^ 2 + x-3 # 나머지는 # = 4x + 5 #

설명:

긴 분열을 해봅시다.

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

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

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

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

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

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

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

몫은 # = x ^ 2 + x-3 # 나머지는 # = 4x + 5 #

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