SOLUTION: Solve a) x^4 - 2x^2 +x +1 / x^2 - 2x +1 Can you please help me out? Thanks so much in advance:) Can you please show the steps it would really help me understand:)

Question 752325: Solve
a) x^4 - 2x^2 +x +1 / x^2 - 2x +1
Can you please help me out? Thanks so much in advance:)
Can you please show the steps it would really help me understand:)
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
No clear simple way to show the process as you could on paper or if we had some other website system. If you know polynomial division, this example is not too bad, ON PAPER. There is a form of synthetic division for a quadratic divisor, but to show on this site, too tough to do.

The lead of the dividend x^4 divided by lead of the divisor x^2:.... x^2 is this partial quotient.

Find x^2*(x^2-2x+1). Subtract from x^4 - 2x^2 +x.

Bring down the next term, "1".
Note, you now have a new leading term in the now revised dividend.

The lead of the current dividend (whateveritis) divided by lead of the divisor x^2:...........(someQ)

Find (someQ)*(x^2-2+1). Subtract from what ever you have of the dividend.

You might or might not have a remainder.
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