A polynomial \(f(x)\) has a factor \((x-a)^2\). Show that \((x-a)\) is a factor of \(f'(x)\).

The equation \(x^3 - 4x^2 - 3x + p = 0\) has two equal roots; find the two possible values of \(p\).

A polynomial \(f(x)\) has a factor \((x-a)^2\). Show that \((x-a)\) is a factor of \(f'(x)\).

The equation \(x^3 - 4x^2 - 3x + p = 0\) has two equal roots; find the two possible values of \(p\).