This sounds tough at first, but once you catch on to the secret, it isn't that difficult. What sort of quadratic has only one solution, given that it always factors into two binomials (well, usually). Easy! It can have only one solution if it factors into the same binomial twice. You can always recognize the candidates because they are "perfect square trinomials", in which both the first and last terms are perfect squares. Alas, most of your answers have that trait. Only A is missing an ending in the first solution. Let's keep looking.
Second, that perfect square would have to be positive so that it could make the same number AND sign twice. There goes solution C. Technically, both B & D would qualify, except that they also specified "standard form", which means descending order. There goes D on a technicality, leaving B. If not for that detail, you would have two different answer sets.