PLEASE HELP?

　
There are a number of problems with this question.

First, a trinomial means nothing.
I assume you mean a quadratic: ax^2 + bx + c

However, some quadratics are not trinomials:
x^2 − 2x ----> a binomial
5x^2 -------> a monomial

In fact, if p = 2 and q = −2, then (x+p) (x+q) = (x+2)(x−2) = x^2 − 4
which is not a trinomial at all

Also, you can have trinomials that are not quadratic:
x^4 − 8x^2 + 16

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Second, when told that (x+p) and (x+q) are factors, this does not necessarily mean they are the ONLY factors.

For example:
2x^2 + 10x + 12 has factors (x+2) and (x+3), but it also has factor 2
2x^2 + 10x + 12 = 2 (x+2) (x+3)

x^4 − 8x^2 + 16 has factors (x−2) and (x+2), but it has 2 factors of each:
x^4 − 8x^2 + 16 = (x−2)^2 (x+2)^2

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Whoever composed this question did a really bad job of it.

Anyway, assuming we have a quadratic polynomial with factors (x+p) and (x+q) ONLY, then just multiply out:

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

Constant term = pq

Answer: B

B. ,A and C are completely irrelevant, and in the formula =(x+p)(x+q), you multiply p and q together.