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

Question

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

jamesj · Answer

x^2 - 4x + 6

anonymous · Answer

how it is factored???

jamesj · Answer

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

anonymous · Answer

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

jamesj · Answer

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

anonymous · Answer

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

jamesj · Answer

attachment

shubhamsrg · Answer

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..

anonymous · Answer

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