Homework help (Basic Algebra-Division of polynomials)

[Krazie]

Please go to the bottom of this page for the problem that I am having trouble with.

[AKG]

Simplify the numerator

\frac{4x^3 - 8x^2 + 5x +1}{x+2}

Now, do you know how to do long division here? Or in general rather, long division of polynomials? I would hope you do, otherwise I don't understand how they can ask this question of you. If you do, then the problem should be easy. If you don't know, I don't know why they'd ask it, and it might be kind of hard to explain it here, as it would be hard to give examples (I don't know if there is latex code that can be used).

[AKG]

Uhh... I see you've edited it. What does this new thing have to do with polynomials or algebra? What is the problem now?

[Krazie]

I am going to try it again. Here is the problem:
\frac{5+5x-8x^2+4X^3-3x^4}{2-x}

[Krazie]

I am coming up with :
-3^3 +4x^2 -8x+5 with a remainder of 117

[Krazie]

I am using short division. I am using only the coeficients in the dividend ordered from highest degree exponent to lowest, divided by the additive inverse of the divisors coeficient. First thing that I do is drop the -3, then multiply the -3 by the divisors coeficient, which is -2. I think that I am doing something wrong there. Can anyone help me?

[eJavier]

Using synthetic div I got

\frac{-33}{2-x}+(19 + 12 x + 2 x^2 + 3 x^3)

I think you're using the same method. If so, you should multiply by 2. Remember that when dividing by x-c you multiply by c.

[ExecNight]

i came up with - (3x^3 + 2x^2 + 12x + 19) - 33 / 2 - x