[Help] Simplify: 2x^4 - 5x^3 - 24x^2 + 13x + 10 over 2x^2 + x +1

Question

anonymous · Answer

$$(2x^4-5x^3-24x^2+13x+10)\div(2x^2+x-1)$$

alekos · Answer

we have to use long division for  a polynomial.  Have you ever done this before?

anonymous · Answer

Yes. I'm quite surprised because in the end I only have 10x left.

anonymous · Answer

My answer is $$x^2-3x-10+\frac{ 10x }{2x^2+x-1}$$

alekos · Answer

it should end up as a quadratic  ax^2 +bx + c  with a possible remainder

alekos · Answer

yeah that looks right but give me five minutes and i'll check your answer

anonymous · Answer

Are we allowed to have a variable of 10x in the remainder? It's my first time to encounter such an equation. I usually end up with a constant/divisor. Instead of a value with a variable/divisor.

alekos · Answer

yes, you're right its normally just a constant but let me get back to you

anonymous · Answer

Okay, sure thing.

alekos · Answer

I get 20x on the numerator of the remainder

alekos · Answer

let me double check my ans

anonymous · Answer

Oops...I'm sorry. I meant 20x, not 10x. Just a type.

alekos · Answer

OK so you're right!

anonymous · Answer

an "x" in the numerator is all right?

alekos · Answer

it sure is

michele_laino · Answer

I confirm that your answer is right! @JustinSpeedster

anonymous · Answer

Okay, thanks a lot guys. :)

alekos · Answer

hey thanks Michele

michele_laino · Answer

:) @alekos