So given $ax^2 + bx + c = dx^2 + ex + f$ and that it holds true for all values of x:
Prove $a = d$, $b = e$, and $c = f$.
What I have done so far is set the equation equal to zero and factor the desired variables together and out:
$ax^2 + bx + c - dx^2 - ex - f = 0$
$ax^2 - dx^2 + bx - ex + c - f = 0$
$(a-d)x^2 + (b-e)x + (c-f) = 0$
Now once I prove that $a - d$, $b - e$, and $c - f$ are all equal to zero, then everything would be all over.
But unfortunately I do not know how to proceed here. I know it probably has to do with polynomial degree root limits or something, but I am fuzzy on the precise procedure and would appreciate the help on finishing this off.