Chapter 8.1, Problem 22PPS

To determine

To find: Whether the expression $c^4-2c^2+1$ 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 22PPS

Yes, it is a polynomial

Degree of the polynomial is $4$

It is a trinomial

Explanation of Solution

Given:

  $c^4-2c^2+1$

Calculation:

The given expression is $c^4-2c^2+1$

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 a whole number and satisfies all the above conditions as well.

Hence, it is a polynomial.

The degree of a polynomial is the highest exponent. So, the degree is $4$

And since, it has three terms. So, it is a trinomial.