Why, according to Polonius, has Hamlet gone mad??is it (a)He grieves too much for his father. (b)He despises Claudius for marring Gertrude (c)He is...

Well, process of elimination as well as Polonius's own
words will quickly answer this question. 

a) Both Claudius
and Gertrude make several comments regarding Hamlet's excessive mourning for his dead
father.  They say this to Rosencrantz and Guildenstern, to Polonius, to each other, and
to Hamlet.  Polonius never says it.

b) Hamlet does, indeed,
despise Claudius for marrying his mother--among other things, of course.  Hamlet says so
to himself, to his freinds, and to his mother.  Even if he believed it, Polonius would
never dare say such a thing to his boss, the king.

d)
Hamlet is envious of anyone who can leave Denmark, the place he has come to see as a
"prison."  This, though, is the least likely answer because it demonstrates the weakest
emotion on the list.  If he really wanted to leave the country he could; he cannot
change his father's death nor his mother's remarrying.

So,
that leaves the correct answer.

c)  Polonius asks Ophelia
to give him anything Hamlet gives her; when she does, he discovers Hamlet's passionate
(though ill-written) love for Ophelia.  In whatever form they were written (as true
expressions of love or as indicators of some melodramatic, overacted passion), Polonius
believes them.  He takes them to the King and hopes to win his favor once again by
solving the mystery of Hamlet's melancholy madness.  In one his most humorous speeches
(IIii), he says: 

readability="5">

"...I have found

The
very cause of Hamlet's
lunacy."

A hundred likes
later, he finally announces that he has commanded his daughter to rebuff any advances or
tokens from Hamlet, which has, in turn, driven him
mad.

"That
she should lock herself from his resort,

Admit no
messengers, receive no tokens,

Which done, she took the
fruits of my advice,

And he, repelled, a short tale to
make,

Fell into a sadness, then into a
fast,

Thence to a watch, thence into a
weakness,

Thence to a lightness, and by this
declension,

Into the madnes wherein he now
raves...."

Clearly Polonius
wants to believe Hamlet is mourning the lost love of his daughter.  It's in his won best
interests to think so, of course, but he also thinks he's been pretty clever in rooting
out the cause when no one else can.