Only divide using the most significant figures ie ?-:color(green)(x^3)
" "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
'~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 1 ")x^4/x^3=color(magenta)(x)
" "color(magenta)(x)
Write as: " "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 2 ")
color(green)(x^3+2x^2-4)
underline(" "color(magenta)(x))" "->"Multiply"
""color(blue)(x^4+2x^3-4x)
Write as:
" "x
" "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
" "underline(color(blue)(x^4+2x^3-4x))" "->" Subtract
" "0+color(red)(x^3)-8x-6" bring down the 6"
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 3 ")
(color(red)(x^3))/(color(green)(x^3)) =color(magenta)(+1)
Write as:
" "x color(magenta)(+1)
" "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
" "underline(x^4+2x^3-4x)" "->" Subtract
" "0+color(red)(x^3)-8x-6
color(green)(x^3+2x^2-4)
underline(" "color(magenta)(+1))" "->"Multiply"
""color(blue)(x^3+2x^2-4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 4 ")
Write as:
" "x +1
" "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
" "underline(x^4+2x^3-4x)" "->" Subtract
" "0+x^3"-8x-6
" "underline(color(blue)(x^3+2x^2-4))" "-> Subtract
These do not line up any more as we have an extra term. For convenience change the order. This can be sorted out later.
Write as:
" "x +1
" "color(green)(x^3+2x^2-4)" |"bar(x^4+3x^3-12x-6)
" "underline(x^4+2x^3-4x)" "->" Subtract
" "0+x^3"-8x-6
" "underline(color(blue)(x^3+0color(white)(.)-4+2x^2))" "-> Subtract
" "0color(white)(.)-8x-2-2x^2 >>>>
The remainder is:" "-2x^2-8x-2 We can not divide any further as its most significant value is less than the x^3 in x^3+2x^2-4
So we express it as (-2x^2-8x-2)/(x^3+2x^2-4) = -(2x^2+8x+2)/(x^3+2x-4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=>(x^4+3x^3-12x-6)/(x^3+2x-4)" " =" " x+1 -(2x^2+8x+2)/(x^3+2x-4)
