Chapter 8.1, Problem 1DGP

To determine

To find: Whether the expression $10x^{-4}-8x^a$ is a polynomial or not. If it is a polynomial, find the degree and determine if it is a monomial, binomial, or trinomial.

Answer to Problem 1DGP

No, it is not a polynomial

Explanation of Solution

Given:

  $10x^{-4}-8x^a$

Calculation:

The given expression is $10x^{-4}-8x^a$

The exponent of a polynomial must be a whole number. For a polynomial, the exponent can never be negative, square root, any fractional number and no variable should be in the denominator.

Here the exponent is $-4$ , which is negative. And a polynomial must not have a negative exponent.

Hence, it is not a polynomial.