Monomial, Binomial or Trinomial

[JoeMaths]

Which expression below represents a binomial or monomial

(a) (x+7)
(b) x+7

 

[Dr.Peterson]

Technically, the first is a monomial, because the parentheses make it a single "term"; the second is a binomial.

But to some extent, what to call it depends on the reason for asking. There are some procedures applicable to binomials that can be applied to either, because they depend not on how it happens to be written at the moment, but on its meaning. The two expressions mean exactly the same thing!

So, what is the context of your question?

 

[JoeMaths]

the context of the question is as follows:
if we agree that (x+7) is a monomial, then does it follow that:
(x+7)(x+2) is a monomial then (x+7)+(x+2) is a binomial?????

 

[Dr.Peterson]

Taken as a conditional statement, the answer has to be yes even if we didn't think (x+7) is a monomial! The same reasoning applies to all three expressions. (But the second "then" doesn't quite make sense grammatically.)

But this doesn't really give a suitable context; the larger question itself needs a context. In what way is the questioner going to be using the answer? How does it matter what is a binomial?