Question

question 13
indicate the answer choice that best completes the statement or answers the question.
determine whether each expression is a polynomial. if it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial.
(6g^{2}h^{3}k)

Explanation:

Step1: Check if it is a polynomial

A polynomial is an expression consisting of variables and coefficients, using only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The expression $6g^2h^3k$ is a product of a coefficient and variables with non-negative integer exponents, so it is a polynomial.

Step2: Find the degree of the polynomial

The degree of a monomial is the sum of the exponents of all its variables. For $6g^2h^3k$, the exponent of $g$ is 2, $h$ is 3, and $k$ is 1 (since $k = k^1$).
$\text{Degree} = 2 + 3 + 1 = 6$

Step3: Classify the polynomial type

A monomial is a polynomial with exactly one term. The expression $6g^2h^3k$ is a single term, so it is a monomial.

Answer:

This is a polynomial. Its degree is 6, and it is a monomial.