Under which of the following operations are the polynomials 3x+2 and 4y-11 not closed

Lets check all the choices:

A. subtraction:

(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13

similarly, (4y-11)-(3x+2)=-3x+4y-13

both are polynomials (of 2 variables)

B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial

C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial

D. 
both  and  are rational expressions in 2 variables, not polynomials

D

Can use look up on internet or no

the diagram shows you   triangle def with de=4, df=9 and de≠df≠ef.

the sum of the lengths of two triangles' sides are always greater than the length of the third side:

de+df> ef (option 54 is false); de+ef> df (option 1 is true); ef+df> de.

substitute sides lengths:

4+9> ef ⇒ ef< 13; 4+ef> 9 ⇒ ef> 5.

then 5< ef< 13 (option 3 is true).

def is a scalene triangle with all sides of different lengths (option 5 is true, option 2 is false).

answer: correct choices are 1, 3 and 5