SOLUTION: Please solve: x^4 - 4x^3 + 3x / x^2 -1 I get x^2 - 4x + 1 - x + 2/x^2

SOLUTION: Please solve: x^4 - 4x^3 + 3x / x^2 -1 I get x^2 - 4x + 1 - x + 2/x^2 - 1

Question 5057: Please solve:
x^4 - 4x^3 + 3x / x^2 -1
I get x^2 - 4x + 1 - x + 2/x^2 - 1
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

First factor out the x from the numerator, and factor the denominator:

Now the trick is this: Is divisible by either (x-1) or (x+1). It turns out (and it usually does!) that it is, in this case, divisible by (x-1). You will have to do synthetic or polynomial division (which I don't know how to do on this website!) as follows:
Divide:
1 | 1 -4 0 3
XXX 1 -3 -3
_____________________
XX 1 -3 -3 0

Other tutors could probably write it better, but basically, the remainder is zero, and the quotient is

Therefore the x-1 divides out leaving this:

By the way, the remaining trinomial does not factor.

R^2 at SCC

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