\( \begin{array}{ll}\text { 11. }(2 x-y)(2 x+y)(3 x-5 x y-y) & \text { 10. } 2(8 p-3 q)\left(p-3+q^{2}\right) \\ \text { 13. }(9 m-n)\left(3 m^{2}-m n+2 n^{2}\right) & \text { 12. }(3 a-2 b)(3 a+2 b)\left(2 a^{2}-4 a b+5 b^{2}\right) \\ \text { 15. } 5(a-b)\left(a^{2}+a b+b^{2}\right) & \text { 14. }(p-5 q)\left(2 p-7 q-q^{2}\right) \\ \text { 17. } 2(3 p+q)\left(9 p^{2}-3 p q+q^{2}\right) & \text { 16. }(2 x-3)\left(4 x^{2}+6 x+9\right) \\ \text { 19. } 3(2 x+1)\left(x^{2}-5 x-1\right) & \text { 18. }-3\left(2 x^{2}-3 x-1\right)(x-2) \\ \text { 19 } & \text { 20. }-2(2 a-5 b)\left(3 a^{2}-a+2 b\right)\end{array} \)

Did you know that factoring polynomials has roots tracing back to ancient Babylon? The early mathematicians used geometrical interpretations of algebra to solve problems related to areas and ratios. This laid the groundwork for methods still in use today, making it one of the oldest mathematical practices that connects us to the minds of the past! In today's world, factoring polynomials is essential for everything from optimizing functions in calculus to simplifying expressions in engineering. By breaking down complex equations, engineers can model systems, analyze data more effectively, and solve real-world problems! Whether you’re designing a bridge or programming an app, mastering these skills can lead to surprisingly satisfying results.