Question

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

Answer 1

x^2 - 4x + 6

Answer 2

how it is factored???

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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..

Answer 8

then

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