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)#
