How do I factorize a polynomial $ax^2 + bx + c$ where $a \neq 1$ How do I factorize a polynomial $ax^2 + bx + c$ where $a \neq 1$?
E.g. I know that $6x^2 + 5x + 1$ will factor to $(3x + 1)(2x + 1)$, but is there a recipe or an algorithm that will allow me to factorize this?

If you know how to factor polynomials for $a=1$, then simply writing
$$ax^2+bx+c=a(x^2+\frac bax+\frac ca )$$
makes the task immediate.
