Question 696108
You wrote x^7-x^4+3x^2-12x+2/6x^5={{{x^7-x^4+3x^2-12x+2/6x^5}}}
 
You most likely meant (x^7-x^4+3x^2-12x+2)/6x^5={{{(x^7-x^4+3x^2-12x+2)/6x^5}}}
{{{(x^7-x^4+3x^2-12x+2)/6x^5=x^7/6x^5+(-x^4+3x^2-12x+2)/6x^5=(1/6)x+(-x^4+3x^2-12x+2)/6x^5}}}
If you are expected to find a quotient polynomial and a remainder polynomial,
{{{highlight(quotient=(1/6)x)}}} and {{{highlight(remainder=(-x^4+3x^2-12x+2)/6x^5)}}}
That is what is usually done with polynomials.
It's like dividing 25 by 8, finding a quotient of 3 and a remainder of 1.
 
You can keep dividing the remainder, as in {{{25/8=3.125}}}, but that is not usually done and ends up in ugly expressions:
{{{(x^7-x^4+3x^2-12x+2)/6x^5=x^7/6x^5-x^4/6x^5+3x^2/6x^5-12x/6x^5+2/6x^5= (1/6)x-(1/6)(1/x)+(1/2)(1/x^3)-2(1/x^4)+(1/3)(1/x^5)}}}
You could write the final expression differently:
{{{(1/6)x-(1/6)(1/x)+(1/2)(1/x^3)-2(1/x^4)+(1/3)(1/x^5)=x/6-1/6x+1/2x^3-2/x^4+1/3x^5=x/6-x^(-1)/6+x^(-3)/2-2x^(-4)+x^(-5)/3}}}
but it does not get much prettier.