The expression x^2 + 5x + 6 is a quadratic polynomial, which is a type of mathematical expression that includes a variable raised to the second power. Quadratic polynomials can be represented in the standard form ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = 5, and c = 6. This specific polynomial can be factored into (x + 2)(x + 3). The roots of the equation, found by setting it equal to zero, are x = -2 and x = -3. These roots represent the points where the graph of the polynomial intersects the x-axis, and the graph is a parabola that opens upwards due to the positive coefficient of x^2.