Polynomials Help Needed!

[JoshwaF]

Hey all!
So I decided to leave my methods stuff 'till last (big mistake) and now it's the last piece of junk that I have to go through and then hopefully get ahead in. Anyway, I'm right at the start of my homework. At the revision stage really, and I still seem to be stuck on a few questions. If anyone could help me out, that'd be awesome! Anyway here's one that I'm stuck on and stay tuned because I'll definitely be back with more.

Given (x+3) and (x-1) are factors of ax^3+bx^2-4x-3, find the values of a and b.

I know I've done plenty of these before but I'm just having mental blank.
Thanks for your help!

[dave101]

Hi,
Use the factor theorem.

As (x+3) is a factor, then P(-3)=0. So you sub in -3 into the 'x'
a(-3^3)+b(-3^2)-4(-3)-3=0
which simplifies to -27a+9b+9=0

Then do the same thing with P(1). Which is
a(1^3)+b(1^2)-4(1)-3=0
simplifies to a+b-7=0

Use simultaneous equations to solve for a and b:
-27a+9b+9=0
 a+b-7=0

a=2,  b=5

[JoshwaF]

Cheers guys! I knew I'd definitely done this before. Have an awesome day both of you.