if bis positive, 'a' can be splited into two no such that sum of those nos is equal to a. keep the sign of a as it is. separate the terms. you will get 4 terms. combine first two and last two. take common.
if b is negative 'a' can be splited into two no such that subtraction of those nos is equal to a.then all same
eg: X^2+3X+2=0
X^2+(2+1)x+2=0
(X^2+2x)+(x+2)=0
x(x+2)+1(x+2)=0
(x+1)(X+2)=0
again,3X^2+X-4=0
3X^2+(4-3)x-4=0
3X^2+4x-3x-4=0
x(3x+4)-(3x+4)=0
(x-1)(3x+4)=0
if co-eff of x^2 is other than 1 , then the sum or subtraction of two no will be the product of co-eff of X^2 and b(see the last eg) all steps including sign convention will be same.