a) False. The sum of 2 and p is 2+p. We don't have any like terms to combine, so we leave this as is. The sum of two (or more) items is the result of adding them. The expression 2p is the result of multiplying 2 and p. If it said "the product of 2 and p is 2p", then it would be a correct statement.
b) True. Any trinomial is a polynomial, but not the other way around. A polynomial has us sum many monomial terms. A trinomial is a special type of polynomial with exactly 3 terms being added.