Let k be added to the polynomial.
Given Equation is p(x) = x^2 - 5x + (4 + k).
If 3 is the zero of the polynomial, then the equation will become p(3) = 0
p(3) = (3)^2 - 5(3) + (4 + k) = 0
9 - 15 + 4 + k = 0
- 6 + 4 + k = 0
-2 + k = 0
k = 2.
Therefore the number to be added to the polynomial is 2.
Hope this helps.