2x+1 is a factor. So we can write
Where m is any number.
So if we equate
We can write;
If product of two numbers is zero, then one of the number must be zero. For example, 6×0=0;
So we assume
(2x+1)=0 or m=0
So if we substitute x=-1/2, then 4x²-kx-k=0 i.e x=(-1/2) is a zero of the polynomial 4x²-kx-k.
Please read carefully 3 or 4 times to understand better.