There are two ways to take this:

"It is false that Shakespeare wrote Hamlet and Longfellow was a poet."

First way:

"It is false that (Shakespeare wrote Hamlet and Longfellow was a poet.)"

~(p ∧ q).

Second way:

"(It is false that Shakespeare wrote Hamlet) and (Longfellow was a poet.)"

~p ∧ q.

Your teacher shouldn't give you ambiguous sentences.

Edwin