In order to factor a polynomial , you have to find its roots . Then, you can write
where is the leading coefficient of
a: Let's try to solve
the disciminant of this quadratic function is
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
This time we can find the two solutions
which yields the factorization