Polynomial simplification is the process of reducing a polynomial expression to its simplest form. This involves combining like terms, which are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x^2 - 2x + 4, the like terms 3x^2 and 5x^2 can be combined to form 8x^2, resulting in a simpler expression of 8x^2 - 2x + 4. Another important aspect of polynomial simplification is factoring, which involves expressing the polynomial as a product of its factors. This can make it easier to solve equations or analyze the polynomial's behavior. For instance, the polynomial x^2 - 5x + 6 can be factored into (x - 2)(x - 3), providing a clearer view of its roots and properties.