Question

when the factors of a trinomial are (x-p) and (x+q) then the constant term of the trinomial is: A. The product of -p and qB. The quotient of -p and q C. The sum of -p and q D. The difference -p and q

Answer 1

In this problem, we want to determine which variables will give us the constant term of the trinomial.

We are given the binomials

`(x-p)(x+q)`

When mutliplying these binomials, we can use the distributive property, or we can use the FOIL method.

Using distribution, we get:

`x(x+q)-p(x+q)`

Distributing the x and p for each term, we have

`x^2+qx-px-pq`

Recall that a constant term is any number that does not have a variable "attached" to it. For example, these are constants:

`4,6,7...`

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.

`x^2+qx-px-\boxed{pq}`

Therefore, the constant term of the trinomial is the product of -p and q.