# Solving $\frac{{2{x^3} - 11x + 6}}{{x - 2}}$ using algebraic juggling

\eqalign{ & \frac{{2{x^3} - 11x + 6}}{{x - 2}} = \frac{{2{x^2}(x - 2) + 4{x^2} - 11x + 6}}{{(x - 2)}} \cr & = 2{x^2} + \frac{{4x(x - 2) - 8x + 11x + 6}}{{x - 2}} \cr & = 2{x^2} + 4x + \frac{{ - 3x + 6}}{{x - 2}} \cr & = 2{x^2} + 4x + \frac{{ - 3(x - 2) - 6 + 6}}{{x - 2}} \cr & = 2{x^2} + 4x - 3 \cr}

I'm a little unsure if my understanding of "algebraic juggling" is correct, I know its similar to long division of polynomials but something in my head isn't sitting right. I'd appreciate it if someone could add something to my understanding, this is how I understand it:

What's being done here is we're finding out how many times $x - 2$ goes into ${2{x^3} - 11x + 6}$, as you work your way through the expressions your answer will be in the form:

dividend/divisor = quotient + remainder/divisor

I'd really appreciate it if someone could break it down for me further and explain precisely what is happening at each step of my answer, especially how the remainder is found to move to the next step, in the "long division" method of polynomials you take away to find the remainder, that doesnt seem to be the case here. Any help would be appreciated.

Thank you.