k) \( 5 x^{2}+15 x+10 \) 1) \( 3 x^{2}-18 x^{2}+24 x \) m) \( 2 x^{4}-12 x^{3}+10 x^{2} \) n) \( x^{3}-10 x^{2}+21 x \) 0) \( 5 x^{3} y+25 x^{2} y+30 x y \)

Did you know that the expression \( 5x^{2} + 15x + 10 \) can be factored to reveal its hidden simplicity? You can pull out a common factor of 5, giving you \( 5(x^{2} + 3x + 2) \), which can further be broken down to \( 5(x + 1)(x + 2) \). This factorization process helps in understanding the zeros of the polynomial! In practical applications, these polynomials represent various phenomena, such as trajectories in physics or profit models in economics. For instance, the equation \( n) \; x^{3}-10 x^{2}+21 x \) could represent a cubic function that describes the volume of a container as a function of its dimensions, helping engineers maximize storage space. Such analyses are invaluable in real-world decision-making!