Factorising a Quadratic

Factorising a quadratic polynomial of the form,

ax² + bx + c = 0

can be done in many depends depending on the values we have for a, b and c. 

Some simple polynomial could be done simply by recognition. For example:

 x² + 4x + 3 = 0

In this scenario we would use the assumption that the factorisation is of the form:

(dx+e)(fx+g) = 0

and we would consider the values of d, e, f and g.

As the coefficient of the x² term is 1, d and f would both be 1. Hence:

(x+e)(x+g) = 0

Now we need numbers for e and g such that:

e*g = 3 and,

e+g = 4

We find that e = 3 and g = 1 or visa versa. 

Hence we can factorise 

x² + 4x + 3 = 0 

to (x+3)(x+1) = 0