# Remainder theorem

• Sep 18th 2007, 07:00 AM
psychocostin
Remainder theorem
Hi all,

I have the fraction:

$(x^4 + 3x^2 - 4)/(x^2 + 1)$

We have been asked to express in mixed number form using i) long division and ii) using the remainder theorem.

Have done the long division bit and got a remainder of -6.
I am not sure how to use the remainder theorem with the x^2 + 1 as if you use f(-1) you get the remainder 0. How do i go about using the remainder theorem with a squared x?

Thanks!
• Sep 18th 2007, 07:12 AM
topsquark
Quote:

Originally Posted by steve@thecostins.co.uk
Hi all,

I have the fraction:

$(x^4 + 3x^2 - 4)/(x^2 + 1)$

We have been asked to express in mixed number form using i) long division and ii) using the remainder theorem.

Have done the long division bit and got a remainder of -6.
I am not sure how to use the remainder theorem with the x^2 + 1 as if you use f(-1) you get the remainder 0. How do i go about using the remainder theorem with a squared x?

Thanks!

Technically you can't use $x^2 + 1$ with synthetic division. However if you set $y = x^2$ then your problem becomes to divide $y^2 + 3y - 4$ by $y + 1$ which can be done by synthetic division.

-Dan
• Sep 18th 2007, 01:57 PM
psychocostin
Remainder theorem
Thanks! I remember doing things like that before. But usually you have to work with y when you've finished.
Do i have to do anything to y when i'm done? Otherwise they might has well just asked me work out the quadratic divided by x + 1.

Does that make any sense?

Many thanks