First, arrange the dividend and divisor from highest to lowest degree of terms. The missing terms will have to be provided with a zero numerical coefficient.
the dividend:
#x^5-x^3-3x^2-12x-7" "#should be
#x^5+0*x^4-x^3-3x^2-12x-7#
the divisor #x-2# is already arranged
Let us divide
#" " " " " " " "underline(" "x^4+2x^3+3x^2+3x-6 " " " " " " " " " " ")#
#x-2" "|~" "x^5+0*x^4-x^3-3x^2-12x-7#
#" " " " " " " "underline(" "x^5-2x^4"" " " " " " " " " " " " " " " " " " " " ")#
#" " " " " " " " " " " " " "2x^4-x^3-3x^2-12x-7#
#" " " " " " " " " " " " " "underline(2x^4-4x^3 " " " " " " " " " " " " " " " " ")#
#" " " " " " " " " " " " " " " " " "3x^3-3x^2-12x-7#
#" " " " " " " " " " " " " " " " " "underline(3x^3 -6x^2" " " " " " " " " " " " ")#
#"" " " " " " " " " " " " " " " " " " " " " " "3x^2-12x-7#
#" " " " " " " " " " " " " " " " " " " " " " underline(3x^2-6x" " " " " " " " " ")#
#"" " " " " " " " " " " " " " " " " " " " " " " " " " " "-6x-7#
#" " " " " " " " " " " " " " " " " " " " " " " " " " ""underline(-6x+12 " " " " ")#
#"" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " "-19larr#remainder
We write the answer in the form
#("Dividend")/("divisor")="Quotient"+("Remainder")/("Divisor")#
#(x^5-x^3-3x^2-12x-7)/(x-2)=#
#x^4+2x^3+3x^2+3x-6+(-19)/(x-2)#
God bless....I hope the explanation is useful.
