Question

question
determine if the expression $-\frac{s^4}{3} - 6ssqrt{7} - s^5$ 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: Recall polynomial definition

A polynomial in variable $s$ is an expression of the form $\sum_{i=0}^{n} a_i s^i$, where $a_i$ are constants, and exponents of $s$ are non-negative integers.

Step2: Analyze each term

1. Term 1: $-\frac{s^4}{3}$ has exponent $4$ (non-negative integer, valid).
2. Term 2: $-6s\sqrt{7}$ has exponent $1$ (non-negative integer, valid).
3. Term 3: $-s^5$ has exponent $5$ (non-negative integer, valid).

All terms meet polynomial criteria.

Step3: Identify type and degree

• Type: It has 3 terms, so it is a trinomial.
• Degree: The highest exponent of $s$ is $5$.

Answer:

The given expression is a polynomial. It is a trinomial of degree 5.