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

Did you know that the polynomial \( x^2 - 5x + 6 \) can be factored into \( (x-2)(x-3) \)? This means its roots, or the x-values that make the equation true, are \( x = 2 \) and \( x = 3 \). It's a handy way to solve quadratics quickly, and helps paint a picture of the function! In real-world applications, such quadratic equations often model trajectory paths, such as the arc of a thrown ball. By setting \( x^{2}-5x+6 = 0 \), you can find where the ball hits the ground (the x-axis), which is essential for sports, engineering designs, and physics experiments alike!