The expression (2p^2 - 2p - 5) is a quadratic polynomial in terms of the variable (p). It can be analyzed for its roots using the quadratic formula (p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), where (a = 2), (b = -2), and (c = -5). This expression can also be factored or graphed to find its characteristics, such as the vertex and axis of symmetry, depending on the context of the problem.