Question

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?

Answer 1

See explanation.

Explanation:

Any expression in a form:

`A_nx^n+A_{n-1}x^(n-1)+...+A_1x+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.