# Thread: Factorise a Quadratic Expression

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.

Please help me out... how this is possible etc.

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

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

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

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

and

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

as required.