Question

determine if the expression $-s^5 + 8s^5t^2$ is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial.

answer attempt 1 out of 3

the given expression dropdown a polynomial.

options in dropdown: represents, does not represent

Explanation:

Step1: Recall Polynomial Definition

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non - negative integer exponents on the variables. In the expression \(-s^{5}+8s^{5}t^{2}\), the variables are \(s\) and \(t\), the exponents of \(s\) are \(5\) (in both terms) and the exponent of \(t\) is \(2\) (in the second term), all of which are non - negative integers. The operations used are addition and multiplication (implicit in the terms like \(s^{5}\), \(t^{2}\) and \(8s^{5}t^{2}\)).

Step2: Determine if it's a Polynomial

Since the expression \(-s^{5}+8s^{5}t^{2}\) satisfies the definition of a polynomial (variables with non - negative integer exponents, combined by addition and multiplication of coefficients and variables), the given expression represents a polynomial.

Answer:

represents