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.

A

Step-by-step explanation:

You had a typo with A, and I think that is the answer as well, seeing as you typed all of your other answers correct, and none of them were labeled open by the first answerer, despite the typo.

If 3 is added to the number: x + 3
b) ...and the sum is tripled.. 
"The sum" is "x + 3" so: 3(x+3)
c) ...the result is 27 more than the number.
27 more than the number is x + 27 
d) Put it all together:
3(x + 3) = x + 27 
Solve for x: 
1) Distribute the left side of the equation:
3x + 9 = x + 27

2) Subtract x from each side of the equation:
2x + 9 = 27
3) Subtract 9 from each side of the equation:
2x = 18
4) Solve for x:
x = 9 
Check: 
1) x = 9
2) 3(x + 3) = x + 27
3) 3 ([9] + 3) = [9] + 27
4) 3(12) = 9 + 27
5) 36 = 36 

So, therefore The answer is correct