(X ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1) nedir?

(X ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1) nedir?
Anonim

Cevap:

Bölüm # = X ^ 2 + a-3 # ve kalan # = 4x + 5 #

Açıklama:

Uzun bir bölüm yapalım

#color (beyaz) (aaaa) ## X, ^ 2 + 2x + 1 ##|##color (beyaz) (aa) ## X, ^ 4 + 3x ^ 3 + 0x ^ 2-x + 2 ##|##color (beyaz) (aa) ## X, ^ 2 + a-3 #

#color (beyaz) (aaaaaaaaaaaaaaaaaa) ## X, ^ 4 + 2x ^ 3 + x ^ 2 #

#color (beyaz) (AAAAAAAAAAAAAAAAAAA) ## 0 + x ^ 3-x ^ 2-x #

#color (beyaz) (aaaaaaaaaaaaaaaaaaaaa) ## + X ^ 3 + 2x ^ 2 + x #

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

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

#color (beyaz) (aaaaaaaaaaaaaaaaaaa) ## 0 + 4x + 5 #

Bölüm # = X ^ 2 + a-3 # ve kalan # = 4x + 5 #

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