The polynomial \(\mathrm{p}\) is such that \(\mathrm{p}(x)=6x^3+x^2-12x+5\).
Find the remainder when \(\mathrm{p}(x)\) is divided by \(x-2\).[1]
Show that \(2x-1\) is a factor of \(\mathrm{p}(x)\).[1]
Hence write \(\mathrm{p}(x)\) as a product of linear factors.[3]
Hence solve the equation \(6\sin^3\theta+\sin^2\theta-12\sin\theta+5=0\) for \(0^\circ\leq\theta\leq90^\circ\).[2]