Quadratic Equation : Factor

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First of all it is good to know that we call the polynomials like the given one and in general like:
ax^2+bx+c

"quadratic" polynomials.

The best method of finding out whether or not we can factor a given "quadratic" polynomial is as follow:

Given: ax^2+bx+c

Find b^2-4ac and discuss:

Case I: If b^2-4ac>0 then the polynomial is factorizable on R (real numbers). To find the factors we first have to find:

x1= (-b+sqrt(b^2-4ac))/(2a); x2= (-b-sqrt(b^2-4ac))/(2a)

then we can definitely factor the given polynomial as follow:

ax^2+bx+c= a(x-x1)(x-x2)

Example: Factor 2x^2+2x-12:

a=2, b=2, c=-12 ---> b^2-4ac= (2)^2-4*(2)*(-12)=100>0 ----> factorizable on R:

x1=(-2+sqrt(100))/(2*2)=8/4=2; ...