Hvad er (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?

Hvad er (x ^ 4 + 3x ^ 3-x + 2) / (x ^ 2 + 2x + 1)?
Anonim

Svar:

Kvoten er # = X ^ 2 + x-3 # og resten er # = 4x + 5 #

Forklaring:

Lad os udføre en lang division

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

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

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

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

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

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

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

Kvoten er # = X ^ 2 + x-3 # og resten er # = 4x + 5 #

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