

By the remainder theorem, the remainder upon dividing a polynomial

by a linear binomial

is equal to

. Via synthetic division, we get
1 | 4 -5 6
. | 4 -1
- - - - - - - - - - -
. | 4 -1 5
which translates to

or

Indeed, when

, the first term on the right hand side vanished and we're left with 5.
C
The construction described creates the incenter of the circle and this point is equidistant from all vertices of a triangle.
The general form would be:

where 'a' is responsible for the magnitude of the function, 'b' is responsible for horizontal shift.and 'c' is responsible for vertical shift of the function.
Your answer would be:

Looks like choice A
The GCF of 36 and 81 is 9
36/9 = 4 water balloons
81/9 = 9 beads
Katrina can invite 9 friends, with each getting 4 water balloons and 9 beads