Factoring the polynomial $6a^4 + a^3b +5a^2b^2 + ab^3 - b^4$ 
can you help me factoring the following polynomial?
$6a^4 + a^3b +5a^2b^2 + ab^3 - b^4$
I don't know where to start from.

Note that $6a^4 + a^3b +5a^2b^2 + ab^3 - b^4$ is homogenous. So set $u=b/a$. Then $6a^4 + a^3b +5a^2b^2 + ab^3 - b^4 = a^4(6 + u +5u^2 + u^3 - u^4)$.
We try integer roots of $6 + u +5u^2 + u^3 - u^4$ by considering the divisors of $6$. We find $6 + u +5u^2 + u^3 - u^4=-(u + 2) (u - 3) (u^2 + 1)$.
This gives
$
6a^4 + a^3b +5a^2b^2 + ab^3 - b^4 = -(2 a + b) (b-3 a) (a^2 + b^2)
$.
