\( \begin{array}{ll}(x+3)\left(x^{2}+x+2\right) & \text { 2. }(a+b)\left(a^{2}-a b+b^{2}\right) \\ (x+2)\left(3 x^{2}-7 x-1\right) & \text { 5. }(3 x+5)\left(2 x^{2}-x-2\right) \\ \left(x+\frac{1}{x}\right)\left(x^{2}-1+\frac{1}{x^{2}}\right) & \text { 8. }(a-b)(a+b)^{2}\end{array} \)

Let's dive into some interesting aspects related to polynomial expressions and factorizations. Did you know that factoring polynomials can be traced back to ancient civilizations? The Egyptians had their own methods, and it was later refined by mathematicians in the Middle Ages. Fast forward to today, and techniques like the distributive property we use now laid the groundwork for modern algebra. This historical evolution shows how our understanding of polynomials has developed! In the real world, factoring polynomials isn't just an academic exercise—it has practical applications too! Engineers use polynomial functions to model everything from the trajectory of a rocket to the behavior of electrical circuits. When optimizing designs or analyzing systems, breaking down complex polynomial expressions into simpler factors helps in understanding and predicting their behavior more efficiently!