Chapter 8.1, Problem 5CYU

To determine

To find: Whether the expression $5m^2{p}^3+6$ 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 5CYU

Yes, it is a polynomial

The degree is $5$

It is a binomial

Explanation of Solution

Given:

  $5m^2{p}^3+6$

Calculation:

The given expression is $5m^2{p}^3+6$

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 all the exponents are whole numbers and the polynomial satisfies all the above conditions as well.

Hence, it is a polynomial.

The degree of a polynomial is the sum of the exponent of variable. So, the degree is given by $\begin{array}{l}2+3\\ =5\end{array}$

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