Question

question determine if the expression $5r^4 - 4r^4s^5$ 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.

Explanation:

Step1: Verify polynomial criteria

A polynomial has terms with non-negative integer exponents on variables, no variables in denominators, no radical variables, and no variable exponents. For $5r^4 - 4r^4s^5$, all variable exponents ($4$, $4$, $5$) are non-negative integers, so it is a polynomial.

Step2: Classify polynomial type

Count the number of terms: $5r^4$ is one term, $-4r^4s^5$ is a second term. A polynomial with 2 terms is a binomial.

Step3: Calculate the degree of each term

• For term $5r^4$: Degree = $4$
• For term $-4r^4s^5$: Degree = $4 + 5 = 9$

Step4: Identify the polynomial degree

The degree of the polynomial is the highest degree of its terms. The highest degree is 9.

Answer:

The expression is a polynomial; it is a binomial with a degree of 9.