what is the simplest form of x^4-4x^3+7x^2-4x+6 -------------------- x^2+1

x^2 - 4x + 6

how it is factored???

how is x^2 - 4x + 6 factored? Use the quadratic formula!

no i am asking for above given expression. i mean how x^2+1 is cancelled out?

Do the long division/synthetic division, what ever you want to call it. It's obvious x^2 is the first term in the division so we have x^2(x^2+1) = x^4 + x^2, subtract that from x^4-4x^3+7x^2-4x+6 and we have -4x^3 +6x^2 - 4x + 6 Next, we want -4x ... and keep going

i do not understand Next, we want -4x ... and keep going how?

you can also do this: in numerator,,break it like this x^4 - 4x^3 + 6x^2 + x^2 - 4x + 6 take x^2 common from first 3 terms and 1 common from last 3.. you get the required ans..

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