The expression x^2 - 5x + 6 is a quadratic polynomial in the variable x. It can be represented in the standard form ax^2 + bx + c, where a = 1, b = -5, and c = 6. Quadratic polynomials are characterized by their parabolic graphs, which can open upwards or downwards depending on the sign of a. To find the roots of this polynomial, we can factor it. The expression can be factored as (x - 2)(x - 3). This means the values of x that make the polynomial equal to zero are x = 2 and x = 3. These roots can also be found using the quadratic formula, which is a method for solving any quadratic equation.