# How do you determine if d+3d^-c is a polynomial and if so, how do you identify if it is a monomial, binomial, or trinomial?

Sep 1, 2017

See explanation.

#### Explanation:

This expression is not a polynomial.

A polynomial of 1 variable is only an expression in a form:

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

where $n$ is a natural number.

In the given expression the first term is a legal term in a polynomial, but the second is not because:

1. it has a variable $c$ in the exponent

2. The exponent has a minus sign

The only legal exponents in a polynomial are natural numbers (or zero)