Which operation is not closed for polynomials? a) (x3 + 8x − 5) (x4 + 6x + 2) b) (x2 + 4x − 5)(8x2 + 3x − 6) c) (6x2 + 2x − 3) + (x2 − 5x + 4) d) −(2x2 + 2x − 5) − (x2 + 2x + 9)

All of the operations that you have listed will produce a polynomial. Therefore, they are all closed for polynomials. (Did you have a typo?)

When we say an operation is closed for a particular problem, we mean that the resulting answer is of the same type as at the beginning.

In these cases, we are starting with polynomials in each problem. After performing the operations, we still have polynomials. Therefore, they are all closed.