Quadratic formula question: Missing multiplying factor of A? I have a very simple problem which must have a simple answer and I was wondering if anyone can point out my error.
I have the following quadratic equation to factor:
$2x^2+5x+1$
Which is of the form:
$Ax^2+Bx+C$
All I want to now do is factor this into the form:
$(x+\alpha)(x+\beta)$
So using the quadratic formula
$x = \frac{-B\pm\sqrt{B^2-4AC}}{2A}$
I get
$x = \frac{-5 \pm \sqrt{17}}{4}$
So I would think then that
$(x - \frac{-5 + \sqrt{17}}{4})(x - \frac{-5 - \sqrt{17}}{4}) = 2x^2+5x+1 $
But it doesn't seem to work. Any x that I choose results in the answer being off by a factor of A (in this case A=2).
What silly thing am I missing?

$Ax^2+Bx+C$ factorize as : $A(x-\alpha)(x-\beta)$ wiht $\alpha + \beta= \dfrac{-B}{A}$ and $\alpha \beta=\dfrac{C}{A}$.
obviously if $A \ne 0$, and  $\alpha$ and $\beta$ are roots of the the two equations:
$$
A(x-\alpha)(x-\beta)=0 \iff Ax^2+Bx+C=0
$$
and
$$
(x-\alpha)(x-\beta)=0 \iff x^2+\dfrac{B}{A}x+\dfrac{C}{A}=0
$$
