The expression x² - 5x + 6 is a quadratic polynomial in the variable x. It can be represented in the standard form ax² + 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 indicate where the graph intersects the x-axis, providing important information about the behavior of the polynomial.