Question

(y^4 – y^3 + 2y^2 + y – 1) ÷ (y^3 + 1) DO NOT INCLUDE PARENTHESES IN YOUR ANSWER

Answer 1

Use long division.

                                     y - 1
         -------------------------------
y³+1  | y⁴  - y³  + 2y²  + y  - 1
          y⁴                    + y
         -------------------------------
               - y³  + 2y²         - 1
               - y³                    - 1
              ---------------------------
                         2y²

Answer:  y - 1 + 2y2 ÷ y³+1

Note:  
The correct answer should be written with parenthesis, as y - 1 + y²/(y³+1) in order to avoid ambiguity.