Can I Factorize an Expression with No GCF?

[Theinvoker]

Hi all,

I was hoping someone could help me with factorizing an expression that has no common factors. I'm working through some pre-module work and I've never come across them before and have no idea where to start!

They are all in the format:

x^2 - ax - b (where there are no common factors for x, a and b)

All I know is that when there are no common factors the GCF is 1, but that's about it :(
Any help or good places to look to get me started are much appreciated.

Many thanks in advance,

Theinvoker :)

 

[malawi_glenn]

if x_1 and x_2 are zeroes to your expression x^2 - ax - b , then

x^2 - ax - b = (x-x_1)*(x-x_2)

 

[Theinvoker]

Thanks for the quick reply. I am still a bit lost tho :(

As an example:

x^2 + 24x +133

I can see the answer is (x + sqrt11+12)(x - sqrt11+12) by using my calculator but can't figure out how to get there.

Many thanks again!

 

[rock.freak667]

For the quadratic equation $ax^2+bx+c=0$

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

 

[Theinvoker]

Ok now I feel like a right idiot lol. Many thanks couldn't see the wood for the trees! :)