Long Division of cubic polynomial

[LearninDaMath]

Homework Statement

\frac{x^3+x^2-5x+3}{x^3-3x+2}

Homework Equations

The Attempt at a Solution

well I'm drawing that long division house with x^3-3x+2 on the outside and x^3+x^2-5x+3 on the inside.

I'm seeing that x^3 goes into x^3 one time, so i put a 1 on top of the "house." then I multiply the 1 by x^3-3x+2 and put the product underneath x^3+x^2-5x+3 . However, I can't subtract or add the numbers because the exponents of the x variables don't line. I'm having a problem with the fact that x^3-3x+2 skips the x^2 exponent. I never did a long division problem where the outstide number skipped an exponent. Should I just make a space like x^3+0-3x+2 and let the x^2 from x^3+x^2-5x+3 drop down - kind of like what i would do if the number under the house x^3+x^2-5x+3 skipped a variable?

 

[Vadermort]

"Should I just make a space like x^3+0-3x+2"
Yes, basically - a better way to visualize it might be
x^3+0x^2-3x+2

 

[LearninDaMath]

Appreciate it. Much thanks on the clarification.

 

[Curious3141]

Homework Statement

\frac{x^3+x^2-5x+3}{x^3-3x+2}

Homework Equations

The Attempt at a Solution

well I'm drawing that long division house with x^3-3x+2 on the outside and x^3+x^2-5x+3 on the inside.

I'm seeing that x^3 goes into x^3 one time, so i put a 1 on top of the "house." then I multiply the 1 by x^3-3x+2 and put the product underneath x^3+x^2-5x+3 . However, I can't subtract or add the numbers because the exponents of the x variables don't line. I'm having a problem with the fact that x^3-3x+2 skips the x^2 exponent. I never did a long division problem where the outstide number skipped an exponent. Should I just make a space like x^3+0-3x+2 and let the x^2 from x^3+x^2-5x+3 drop down - kind of like what i would do if the number under the house x^3+x^2-5x+3 skipped a variable?

In this case, the quickest method to do it is as follows: factorise the denominator. There's a linear factor in common between numerator and denominator. Divide the numerator by that factor using a shortcut like Ruffini's synthetic division (should be in the tutorials section, I think, if not, google it). After you do that, divide the resulting quadratic by other factor using Ruffini's method again and get the quotient and remainder.

If you're really required to show the full long division, you have no choice, but if you just need a quick result, the above is a fast and accurate method.