Question

determine if the expression $-x^{3} + \frac{w^{2}}{9} + w^{5}\sqrt{7}$ 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 \\(\quad\\) a polynomial.

Explanation:

Step1: Recall polynomial definition

A polynomial is an expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Step2: Analyze each term

• Term1: $-x^3$: Non-negative integer exponent, valid.
• Term2: $\frac{w^2}{9} = \frac{1}{9}w^2$: Non-negative integer exponent, valid.
• Term3: $w^5\sqrt{7} = \sqrt{7}w^5$: Non-negative integer exponent, valid.

All terms follow polynomial rules.

Step3: Identify polynomial type

It has three distinct terms, so it is a trinomial.

Step4: Find the degree

The highest exponent of the variables is 5 (from $w^5\sqrt{7}$).

Answer:

The given expression is a polynomial. It is a trinomial, and its degree is 5.