From the given
#(4z^4-11z^3+27z^2-39z-25)/(z^2-z+6)#
You can see that the terms are arranged from highest degree to the lowest degree already. So we can divide at right away at once
#" " " " " " " " underline(+4z^2-7z-4" " " " " " " " " " " " )#
#z^2-z+6|~4z^4-11z^3+27z^2-39z-25#
#" " " " " " " " underline(+4z^4-4z^3+24z^2" " " " " " " " " " )#
#" " " " " " " " " " " " ""-7z^3+3z^2-39z-25" " " " " " " " " " " " #
#" " " " " " " " " " " " underline(-7z^3+7z^2-42z" " " " " " " " )#
#" " " " " " " " " " " " " " " " " "-4z^2+3z-25" " " " " " " " " " " " #
#" " " " " " " " " " " " " " " " " " underline(-4z^2+4z-24" " " " " " " " )#
#" " " " " " " " " " " " " " " " " " " " " " " "-z-1" " " " " " " " " " " " #
Write the answer this way
#"Dividend"/"Divisor"="Quotient"+("Remainder")/("Divisor")#
#(4z^4-11z^3+27z^2-39z-25)/(z^2-z+6)=4z^2-7z-4-(z+1)/(z^2-z+6)#
God bless....I hope the explanation is useful.
