Question

determine if the expression $3r^5 + 8r^3$ is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial. answer attempt 1 out of 2 the given expression a polynomial. submit answer

Explanation:

Step1: Recall polynomial definition

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non - negative integer exponents of variables. In the expression \(3r^{5}+8r^{3}\), the variable is \(r\), the exponents of \(r\) are \(5\) and \(3\) (both non - negative integers), and the operations are addition and multiplication of coefficients with the variable. So, it satisfies the definition of a polynomial.

Step2: Determine the type of polynomial

The number of terms in the polynomial \(3r^{5}+8r^{3}\) is 2. A polynomial with two terms is called a binomial.

Step3: Determine the degree of the polynomial

The degree of a polynomial is the highest power of the variable in the polynomial. For the terms \(3r^{5}\) (power of \(r\) is 5) and \(8r^{3}\) (power of \(r\) is 3), the highest power is 5. So, the degree of the polynomial is 5.

Answer:

The given expression is a polynomial. It is a binomial (type) with degree 5. For the first blank in the original problem (the dropdown), the answer is "is".