Write a trinomial that can be factored as (x+p)(x+q) where p and q are positive numbers?

Just multiply them out, and substitute any values for p and q that you want. What's the problem???

You can simplify that expression to:

= x^2 + (q+p)x + pq
= x^2 + qx + px + pq

But you can't really simplify that to a trinomial without knowing the values of at least two of the variables. For example, if you know what p and q are, you can simplify p + q to a single number, so (p+q)x becomes a single term. But right now it's NOT a single term, so you have a 4-term polynomial, not a trinomial.

x^2+(p+q)x+pq