## Polynomial and quadratic homework help!

### kirsty*

Posted 09 January 2012 - 12:04 PM

I'm new to this, but i was hoping someone would be able to help me with ths problem I've been stuck on I know it is to do with synthetic division but I'm unsure how to answer it,

When 2x^3+px^2+qx-1 is divided by (x+1), the remainder is 2>
Given that (x-2) is a factor of x^3+qx^2+px-6, find the values of p and q.

If anyone could help I would really appreciate it!

Thank you.

### Marcus

Posted 09 January 2012 - 12:42 PM

Yes you are right, it involves two synthetic divisions:
firstly use synthetic division dividing x+1 into 2x³+px²+qx-1 and letting the remainder (the bottom right number) equal 2.
You should end up with p-q-3=2 =>
p-q=5 (1)

second divide x-2 into x³+qx²+px-6, this time letting the remainder equal 0
so we get 2p+4q+2=0 =>
p+2q=-1 (2)

The using simultaneous equations on eqns 1 and 2 you get that p=3 and q=-2

If you need me to go through the synthetic divisions step by step I can, but try them on your own first, just take them slow and make sure you leave a lot of room between numbers cos the expressions can get long XD

Hope this helps

### kirsty*

Posted 09 January 2012 - 06:41 PM

Thank you so much!!! this has helped loads .