Factoring Quadratics

Question

What is the best way to factor a quadratic function with a leading coefficient that is bigger than 1?

for ex:

2x^2 - 5x -3

Answer 1

by multiplying the leading coefficient and the constant term we get -6.

we use this value to manipulate the coefficient of x:

2x^2-5x-3 becomes 2x^2 - 6x + x - 3

This is now a problem factorable by grouping:

(2x^2 - 6x) + (x - 3) = 2x(x - 3) + (x - 3) = (2x + 1)(x - 3) :)