Hey everyone, I know this is probably basic for you but I really can't understand this.

This is the lesson I've been following.

I have learned to Factorise the Quadratic Equations which is (Factoring $\displaystyle ax^2 + bx + c : a=1)$ on that website, I think thats pretty easy, But for some reason I really dont understand the next part which is (Factoring $\displaystyle ax^2 + bx + c : a>1$)

I think I understand what it's trying to get to, but I just can't get my head around it.

Does anyone have any easier or alternative ways of understanding this ?
Thanks.

2. There's an easier way. Multiply your $\displaystyle a$ and $\displaystyle c$ values together. You need to find two numbers that multiply to become $\displaystyle ac$ and add to become $\displaystyle b$.

To use the examples on that page...

$\displaystyle 2x^2 + 13x - 7$.

Multiplying our $\displaystyle a$ and $\displaystyle c$ values gives $\displaystyle -14$. So we need two numbers that multiply to give $\displaystyle -14$ and add to be $\displaystyle 13$. They are $\displaystyle 14$ and $\displaystyle -1$.

So we break up the middle value into $\displaystyle 14x - 1x$ and then factorise by grouping.

$\displaystyle 2x^2 + 13x - 7 = 2x^2 + 14x - 1x - 7$

$\displaystyle = 2x(x + 7) - 1(x + 7)$

$\displaystyle = (x + 7)(2x - 1)$.

The second example...

$\displaystyle 6x^2 - 19x + 3$.

Multiply the $\displaystyle a$ and $\displaystyle c$ values, we get $\displaystyle 18$. So we need two numbers that multiply to give $\displaystyle 18$ and add to $\displaystyle -19$. They are $\displaystyle -18$ and $\displaystyle -1$.

Break up the middle term into $\displaystyle -18x - 1x$...

$\displaystyle 6x^2 - 19x + 3 = 6x^2 - 18x - 1x + 3$

$\displaystyle = 6x(x - 3) - 1(x - 3)$

$\displaystyle = (x - 3)(6x - 1)$.

Is this clearer now?

3. Thank you so much!
This is much clearer, I'll run through some more equations when I get home from work.
This is much easier to understand thank you!