\( \left. \begin{array} { l }{ f ( x ) = ( x - 2 ) ( 2 x ^ { 2 } + 5 x - 12 ) } \\ { = ( x - 2 ) } \end{array} \right. \)

The function you have there, \( f(x) = (x - 2)(2x^2 + 5x - 12) \), showcases the beauty of polynomial expressions! The term \( (x - 2) \) indicates a factor, which tells us that \( x = 2 \) is a root of the polynomial. This means that the function will cross the x-axis at \( x = 2 \), making it crucial if you're looking for quick insights into the graph's behavior. To dive deeper into real-world applications, this function can represent various physical phenomena. For example, if you think about the trajectory of projectile motion, the factors can signify important points such as the moment it reaches the ground (when \( f(x) = 0 \)). Analyzing such functions helps in optimizing designs or processes, like finding the ideal angle for launching an object for maximum distance!