Question

M^5n^2+mn^2+n^6Select all choices that apply.A) The degree of the polynomial is 5 B) The degree of the polynomial is 6C) The degree of the polynomial 7 D) The polynomial is a monomialE) The polynomial is a binomialF) The polynomial is a trinomial

Answer 1

For the given expression:

`m^5n^2+mn^2+n^6`

Recall that a monomial is an algebraic expression that involves multiplications and exponentiations, and is separated from other monomials through a "+" or "-" sign. Then, the given expression has three monomials, which makes it a trinomial.

On the other hand, for polynomials in two or more variables, the degree is equal to the maximum degree among its terms, and the degree of a single term is the sum of the exponents of the variables in the term.

The first term has a degree of 7, the second term has a degree of 3 and the third term has a degree of 6. Then, the degree of the whole trinomial is 7.

Therefore, two options apply for the given expression:

`\begin{gathered} C)\text{ The degree of the polynomial is 7} \\ F)\text{ The polynomial is a trinomial} \end{gathered}`