Math

QuestionIs n4+n2m72m5n^{4}+\frac{n^{2} m}{7}-2 m^{5} a polynomial? If yes, state its type and degree.

Studdy Solution

STEP 1

Assumptions1. The expression given is n4+nm7m5n^{4}+\frac{n^{} m}{7}- m^{5}

STEP 2

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

STEP 3

The given expression n+n2m72m5n^{}+\frac{n^{2} m}{7}-2 m^{5} involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Thus, it can be considered as a polynomial.

STEP 4

The degree of a polynomial is the highest power of the variable in the polynomial.

STEP 5

In the given polynomial, the terms are n4n^{4}, n2m7\frac{n^{2} m}{7}, and 2m5-2 m^{5}.

STEP 6

The degree of the term n4n^{4} is4, the degree of the term n2m\frac{n^{2} m}{} is3 (2 from n2n^{2} and1 from mm), and the degree of the term 2m5-2 m^{5} is5.

STEP 7

The highest degree among all the terms is5, which is the degree of the polynomial.

STEP 8

The type of the polynomial is determined by the number of terms in the polynomial. Since there are three terms in the polynomial, it is a trinomial.
The expression n4+n2m72m5n^{4}+\frac{n^{2} m}{7}-2 m^{5} is a polynomial. It is a trinomial of degree5.

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