In order to factor a polynomial [tex]P(x)[/tex], you have to find its roots [tex]x_1,x_2,\ldots,x_n[/tex]. Then, you can write
[tex]P(x)=a(x-x_1)(x-x_2)\ldots(x-x_n)[/tex]
where [tex]a[/tex] is the leading coefficient of [tex]P(x)[/tex]
a: Let's try to solve
[tex]12u^2+5u+3=0[/tex]
the disciminant of this quadratic function is
[tex]\Delta = b^2-4ac=25-144=-119[/tex]
So, this quadratic function has no roots, which implies that it cannot be factorised (using real numbers, at least. Are you allowing complex numbers? Let me know in that case)
b: Similarly, we set up
[tex]50g^2 - 15g - 2=0[/tex]
This time we can find the two solutions
[tex]g_1 = -\dfrac{1}{10},\quad g_2=\dfrac{2}{5}[/tex]
which yields the factorization
[tex]50g^2 - 15g - 2=50\left(g+\dfrac{1}{10}\right)\left(g-\dfrac{2}{5}\right)[/tex]
