factoring polynomial of degrees higher than 2 is tricky

you need to do some trial and error to start with and try to find at least one

if the polynomial to be factored is f(x), try to test one root for f(x) = 0 at least

this is not straightforward

in this case if you divide -3 first, you get the coefficient for highest degree as 1 and the constant becomes 4

a theorem states that the factors of constant term might be the roots, in this case, 1, 2, 4 (including -ve values as well)

however after testing none of them is a root

actually this polynomial does not have integer roots and can't be factored