High School

Determine if the expression \((5r^4 - 4r^4s^5 + 5r^4 - 4r^4s^5)\) is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.

A. Polynomial of degree 53
B. Polynomial of degree 60
C. Not a polynomial
D. Polynomial of degree 62

Answer :

Final answer:

The given expression (5r⁴ - 4r⁴s⁵⁵r⁴ - 4r⁴s⁵) is a polynomial of degree 62. So, the correct answer is d.

Explanation:

The given expression (5r⁴ - 4r⁴s⁵⁵r⁴ - 4r⁴s⁵) is a polynomial.

A polynomial is an algebraic expression with one or more terms, where each term is a product of a constant and one or more variables raised to non-negative integer exponents.

The given expression has three terms: 5r⁴, -4r⁴s⁵⁵r⁴, and -4r⁴s⁵. Therefore, it is a polynomial.

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the degree of the polynomial is 4 because the highest power of the variable (r) is 4.

So, the correct answer is d) Polynomial of degree 62.