Factoring the Quadratic Polynomial $a x^2 +b x +c$

I want mathematica to factor the quadratic polynomial $a x^2 +b x +c$ into this standard form $a(x-r_1)(x-r_2)$ with $r_1=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}$ and $r_2=-\frac{b}{2a}-\frac{\sqrt{b^2-4ac}}{2a}$. I tried Factor and its Extension option but I could not get anyting.

• Try factorCompletely[a x^2 + b x + c, x] from Daniel's answer to the question @Artes linked. – Michael E2 Mar 7 '18 at 17:29
• – Artes Mar 7 '18 at 17:33

a Times @@ (y - # & /@ (x /. Solve[a x^2 + b x + c == 0, x]))

• (+1) Thanks. :) But, why they really made Factor? :D Also, you missed the coefficient $a$. :) – H. R. Mar 7 '18 at 17:13