In this problem, we want to determine which variables will give us the constant term of the trinomial.
We are given the binomials
[tex](x-p)(x+q)[/tex]
When mutliplying these binomials, we can use the distributive property, or we can use the FOIL method.
Using distribution, we get:
[tex]x(x+q)-p(x+q)[/tex]
Distributing the x and p for each term, we have
[tex]x^2+qx-px-pq[/tex]
Recall that a constant term is any number that does not have a variable "attached" to it. For example, these are constants:
[tex]4,6,7...[/tex]
However, this is an abstract example. So for our purposes, the only true variable will be x, while p and q represent some unknown real numbers.
Since x is our variable, we see only the last term has no x attached to it.
[tex]x^2+qx-px-\boxed{pq}[/tex]
Therefore, the constant term of the trinomial is the product of -p and q.
