# How do you determine if a-a^2 is a polynomial and if so, how do you identify if it is a monomial, binomial, or trinomial?

Nov 7, 2017

See explanation.

#### Explanation:

Any expression in a form:

${A}_{n} {x}^{n} + {A}_{n - 1} {x}^{n - 1} + \ldots + {A}_{1} x + {A}_{0}$

is a polynomial of variable $x$.

The expression given can be written as:

## $a - {a}^{2} = - {a}^{2} + a$

So it is in the form given above, so it is a polynomial.

To determine if it is a mono-, bi-, or trinomial you have to check the number of elements in the sum. Here we have 2 elements: $- {a}^{2}$ and $a$, so the expression is a binomial.