Let $p(y) = y^2 -5y + 6$. Now, if $p(y) = (y -a) \,(y -b)$, you know that the constant term will be $ab$. So, $ab = 6$. So, to look for the factors of $p(y)$, we look at the factors of $6$.

The factors of $6$ are $1, \,2$ and $3$.

Now,            $p(2) = 2^2 -(5 \times 2) + 6 = 0$

So,                $y -2$ is a factor of $p(y)$.

Also,             $p(3) = 32 -(5 \times 3) + 6 = 0 $

So,                $y -3$ is also a factor of $y^2 -5y + 6$.