Why is $f(x) = 4x + xz + 400$ not a trinomial function? Here's the function:
$$f(x) = 4x + xz + 400$$
I don't know why that's not a trinomial function. There are $3$ terms separated by a "$+$".
 A: A trinomial is a polynomial consisting of three terms or monomials. A monomial is a polynomial with just one term. The general form of a quadratic trinomial is
$$f(x)=ax^2+bx+c$$
The function
$$f(x)=4x+xz+400=x(4+z)+400$$
is a polynomial with two terms (i.e. it is binomial) simply because $f(x)$ is a function which only depends on the variable $x$ (meaning that the dependent variable is defined to be $f(x)$ and not $f(x, z)$), hence the term $x(4+z)$ is a monomial. 
However, if the function was defined as
$$f(x) = x^2 + 4x + 400$$ 
then $f$ would be a trinomial since both $x^2$ and $4x$ vary as $x$ changes. 
A: $4x+xz+400$ is a trinomial, if you ask me. So would be $x+x+x$. "Trinomial" just means having three terms, and the way either thing is written, it has three terms.
It strikes me as incorrect to call a function "trinomial". It's a property of what you write, not what mathematical object it is. $x+x+x$ is a trinomial and $3x$ is a monomial. The function $f$ that triples its input is neither trinomial nor monomial, because those adjectives should apply to expressions written a certain way, not to functions.
