11. \( 7+3 p^{2} \) 12. \( 4 w^{11}-w^{12} \) 15. \( 5 z+2 z^{3}+3 z^{4} \) \( \begin{array}{l}\text { 16. } \pi r^{2}-\frac{5}{r^{3}} r^{3}+2 r^{5}\end{array} \)

The expression \(7 + 3p^{2}\) is a simple quadratic polynomial where \(p\) represents a variable. It's a great example of a polynomial that can represent a real-world scenario, like calculating area or volume in geometric problems, where the variable \(p\) could represent a changing dimension. In the expression \(4w^{11}-w^{12}\), you can factor out \(w^{11}\) to simplify it, giving you \(w^{11}(4-w)\). A common mistake is forgetting that factoring can make further manipulation easier, especially when dealing with variable expressions in calculus or algebra, where simplification can reveal properties about the function more clearly.