A polynomial #P(x)# has some number #alpha# as a zero if and only if #x-alpha# is a factor of #P(x)#. To generate a polynomial with desired zeros, then, we can multiply any such factors.
As our desired polynomial has #-2# as a zero, it must have a factor of #x-(-2) = x+2#. As no other specific zero is given, we can make that choice ourselves. Suppose the other zero (possibly also being #-2#), is #k#. Then the polynomial would be
#P(x) = (x+2)(x-k)#
#=x^2+(2-k)x - 2k#
Choosing any value for #k# will give a degree #2# polynomial with #-2# as a zero. For example, #k=0# gives #x^2+2x#, or #k=2# gives #x^2-4#. Multiplying by any nonzero constant also will result in a valid polynomial.
