\( \left. \begin{array} { l } { ( m + 9 ) ( m - 3 ) } \\ { m ^ { 2 } - 12 m + 27 } \\ { m ^ { 2 } + 6 m - 27 } \\ { m ^ { 2 } - 6 m + 27 } \\ { m ^ { 2 } + 12 m - 27 } \end{array} \right. \)

Did you know that factoring polynomials like \( (m + 9)(m - 3) \) gives you insight into the roots of the polynomial? This expression can be expanded to reveal its quadratic form, \( m^2 + 6m - 27 \), showcasing the relationship between the roots and the coefficients of the equation. Those roots, in this case, are exactly \( m = -9 \) and \( m = 3 \)! In real-world applications, factoring quadratics is essential in various fields like engineering and physics, where equations must be simplified to solve real-life problems. For example, in projectile motion, the maximum height can be modeled by a quadratic equation, and factoring could help identify crucial points like maximum height and time of flight, making the concept not just theoretical but practically indispensable!