First, you should simplify the function expression.
3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k
In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder. The first two terms clearly divide by x. However, the last two do not. In order for this to work out where k is constant, 5k would have to cancel out the +15 term, leaving nothing to divide by x.
So: 15 + 5k = 0
5k = -15
k = -3
