Unknown coefficients of a cubic with a quadratic factor, its roots and a remainder

The cubic polynomial \(\mathrm{P}(x)=px^3+qx^2-13x-6\), where \(p\) and \(q\) are constants, has \(x^2-x-6\) as a factor.

1. Find the value of \(p\) and the value of \(q\).[4]
2. Find all three roots of the equation \(\mathrm{P}(x)=0\).[2]
3. Find the remainder when \(\mathrm{P}(x)\) is divided by \(x-2\).[1]