David performed the following mathematical operation

B) 1 must be the root of the polynomial .

Step-by-step explanation:

We are given that polynomial is being divided by factor (x-1).

It is also said that when David perform the mathematical operation it gives remainder 0 .

Remainder 0 represents that divisor (x-1) is a factor polynomial .

As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.

Therefore,

x-1=0

Adding 1 on both sides, we get

x-1+1= 0+1

x=1.