Find the GCD of ... Find the GCD of:
$y^2-10y+24+6x-9x^2$, $2y^4-18x^2y^2-48xy^2-32y^2$.
My Attempt:
$$
\begin{split}
1^{st} \text{expression} &= y^2-10y+24+6x-9x^2\\
&={(y)^2-2\cdot(y)\cdot5+(5)^2}-(5)^2+24+6x-9x^2\\
&=(y-5)^2-{25-24-6x+9x^2}\\
&=(y-5)^2-{(1)^2-2\cdot(1)\cdot(3x)+(3x)^2}\\
&=(y-5)^2-(1-3x)^2\\
&=(y-5+1-3x)(y-5-1+3x)\\
&=(y-3x-4)(y+3x-6).
\end{split}
$$
But, I could not factorize the $2^{nd}$ expression. Please help.

You don't need to factor that quartic expression from scratch; you just have to try out all factors of the quadratic expression.
Use synthetic division to see that 
$$
\frac{2y^4-18x^2y^2-48y^2x-32y^2}{y-3x-4} = 2y^2(y+3x+4)
$$
So the GCD is $(y-3x-4)$.
