Factor: \( x^{2}-5 x+6 \)

To factor the quadratic expression \( x^{2}-5x+6 \), we need to find two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of the linear term). The numbers -2 and -3 fit the bill perfectly, as \(-2 \times -3 = 6\) and \(-2 + -3 = -5\). Thus, we can express the factored form as \( (x - 2)(x - 3) \). Another way to visualize this is to think of the quadratic as a shape. When you "cut" it into its factors, you can see it as the area formed by two rectangles, where the lengths are \( x - 2 \) and \( x - 3 \). This reinforces the idea that factoring not only simplifies expressions but connects them to geometrical interpretations!