Question

Pretty dumb to ask, but how do you divide:
x^4 +5x^3 -2x^2 +5x -3 by x^2 +1?

Answer 1

HOW do you divide it is what i'm asking..

Answer 2

\[\frac{ x^4 + 5x^3 - 2x^2 + 5x - 3 }{ x^2 + 1 }\]

Answer 3

....yes. I know that.
what would the simplified form be...

Answer 4

dumber ans would be --> you simple dont! ;)

Answer 5

and the smarter thing would be ,, long division..

Answer 6

are you familiar with polynomial division @breberea ?

Answer 7

Not at all. I normally do synthetic, but I don't know how to do that with x^2+1..

Answer 8

you make a point...

Answer 9

like @Aryang said...you simply dont

Answer 10

synthetic can only be done with linear dividends...in this case you have quadratic...so you can't use synthetic

Answer 11

you should just use long division

Answer 12

@lgbasallote that's the thing. I don't know how to do long division with equations like this. That's why I said it's pretty dumb..

Answer 13

if you want to avoid lengthy work,,you may simply numerator,, for example
in x^4 +5x^3 -2x^2 +5x -3 we can write it as
x^4 + x^2 + 5x^3 - 3x^2 + 5x -3
now first 2 terms here are divisible by x^2 +1
rest you have
5x^3 - 3x^2 + 5x -3
= 5x^3 + 5x - 3x^2 - 3
again first 2 terms are divisible by x^2 + 1

rest remaining is
-3x^2 - 3 = -3(x^2 +1)

hope that helped..

Answer 14

@Aryang I'm sure you're right, but I cant do it like that.
It's either:
f(x) = (x2 + 1)( x2 + 5x - 3)

f(x) = (x2 + 1)( x2 + 5x - 3) - 15x - 9

f(x) = (x2 + 1)( x2 - 5x - 3) - 15x - 9

f(x) = (x2 + 1)( x2 - 5x - 3)