How to factor ax2 bx c?

In the same way as you could factor trinomials on the form of

x2 + bx+c x2 + bx+c

You can factor polynomials on the form of

a x2 + bx+c a x2 + bx+c

If a is positive then you just proceed in the same way as you did previously except now

a x2 + bx+c = (x+m) (ax+n) a x2 + bx+c = (x+m) (ax+n)

where c=mn, ac=pq and b=p+q=am + n