Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2? a) 3x2 − 11x + 8 may or may not be a polynomial b) 3x2 − 11x + 8 will be a polynomial c) 3x2 − x + 4 may or may not be a polynomial d) 3x2 − x + 4 will be a polynomial tip: every 2 after 3x is an exponent.. so it would be 3x^2

Choice B
3x^2 - 6x + 2 will be a polynomial



Explanation:

Line up the terms and subtract straight down
3x^2 - 6x + 2
           5x  - 6

3x^2 -11x + 8

this is a polynomial as it is a sum of three monomials

Subtraction of any two polynomials will result in another polynomial. This is what closure means. In math terms, closure is the idea of taking two objects and performing some operation on them (eg subtraction). If we get the same type of object back, then the set of considered closed under that operation.

Here's another example of closure. Take two glasses of water and pour them together. The two glasses can be of different shapes and sizes. It doesn't matter. The fact that we have two containers of water is all that matters. In this example,the water is like the polynomial. Combining the two containers of water into one will result in a greater amount of water. Combining water with water leads to more water. 

Answers4.) -1/205.) -1/406.) -55/127.) -3/4