Solve \(x^{2} - 2x - 8 > 0\).

If (x + 3) is a factor of the polynomial \(x^{3} + 3x^{2} + nx - 12\), where n is a constant, find the value of n.

The line \(y = mx - 3\) is a tangent to the curve \(y = 1 - 3x + 2x^{3}\) at (1, 0). Find the value of the constant m.

The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation. 

Given \(\sin \theta =  \frac{\sqrt{3}}{2}, 0° \leq \theta \leq 90°\), find \(\tan 2\theta\) in surd form.