1. ## Factorise a Quadratic Expression

based on this text:
How to Factorise a Quadratic Expression | eHow.com

You factorise the quadratic expression x²+ (a+b) x +ab by rewriting it as the product of two binomials (x+a) X (x+b). By letting (a+b)=c and (ab)=d, you can recognize the familiar form of the quadratic equation x²+ cx+d. Factoring is the process of reverse multiplication and is the simplest way to solve quadratic equations.

But I found an equation which has solutions and is not congruent with the above text, like:

6x^2+5x-4=0

Since the solution is: (2x-1)(3x+4)

Based on the above text means, (a*b)=d --> (-1*4)= -4 ok but;
(a+b)=c --> (-1+4)= 3 is not ok sine in the equation is 5.

2. The above fact works only if the leading coefficient is 1. That is you must have an equation of the form $x^2+ cx+d$. But don't worry. You can do that just by dividing the 6 out. You get

$\displaystyle x^2+\frac{5}{6}x-\frac{4}{6} = 0$

from here $\displaystyle a+b= \frac{5}{6}$ and $\displaystyle ab =\frac{4}{6}$

$\displaystyle-\frac{1}{2}\times\frac{4}{3} = -\frac{4}{6}$

and

$\displaystyle-\frac{1}{2}+\frac{4}{3} = -\frac{3}{6}+\frac{8}{6} = \frac{5}{6}$

as required.