4) \( 2 x^{2}-5 x+2 \)

To dive into the world of this wonderful quadratic expression, let's explore how it factors! The polynomial \( 2x^2 - 5x + 2 \) can be factored using the AC method. Multiply the leading coefficient (2) by the constant term (2) to get 4. You then need to find two numbers that multiply to 4 and add to -5, which are -4 and -1. This leads us to the factors: \( (2x - 1)(x - 2) \). Voila! Now, let's see how this quadratic might pop up in everyday life! Quadratics like this one can be used in various real-world applications, from physics problems involving projectile motion to optimizing dimensions in business. For example, if you're trying to maximize the area of a rectangle with a given perimeter, the dimensions could easily lead you back to a quadratic equation similar to \( 2x^2 - 5x + 2 \). So next time you see a quadratic, remember—it's not just math; it's all around you!