Chapter 8.1, Problem 25PPS

To determine

To find: Whether the expression $5n^3+n{q}^3$ 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 25PPS

Yes, it is a polynomial

Degree of the polynomial is $4$

It is a binomial

Explanation of Solution

Given:

  $5n^3+n{q}^3$

Calculation:

The given expression is $5n^3+n{q}^3$

The exponent of a polynomial must be a whole number. For a polynomial, the exponent can never be negative, square root, any fractional number, no variable 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. There are two variable in this polynomial. So, the degree is the sum of the exponent of these two variables.

Hence, the degree is $1+3=4$

And since, it has two terms. So, it is a binomial.