1) \( -20 r^{3}+30 r+20 \)

Did you know that polynomials like \( -20 r^{3}+30 r+20 \) have rich histories dating back to ancient civilizations? Mathematicians from Babylon to Greece explored these algebraic expressions, though they often used different notations. The term "polynomial" itself is derived from the Latin words "poly" (many) and "nomial" (terms), giving these mathematical expressions their name! When working with polynomials, it's common to forget to check for common factors, which can simplify your life significantly! In this case, notice that all terms share a common factor of 10. Factoring out the 10 could lead you to \( 10(-2r^3 + 3r + 2) \), making further operations like finding roots or applying the polynomial long division much easier. Keep checking for those hidden gems!