Question

Is 5m^3 -3m^4-7m a polynomial? State the type and degree of the polynomial.

Answer 1

Yes it is a polynomial.

It is a trinomial.

The degree is 4.

Explanation:

So polynomial is an expression that has variables, constants, and exponents. And all of these are connected through things like addition and subtraction. In this question, you have x as your variable, 0 as your constant, and 4,3,1 as your exponents.

A term is the part of the polynomial that is separated by + or - sign. So in this question, you have 5m^3, -3m^4, and -7m as your terms. Because you have three terms, therefore this is a trinomial.

The degree of polynomial is represented by the variable with the largest exponent, so in your case, 4 is your largest exponent, therefore the degree of the polynomial is 4.

Answer 2

The expression 5m^3 -3m^4-7m is indeed a polynomial. Specifically, it is a trinomial of the 4th degree, where the largest exponent of the variable m is 4.

Yes, 5m^3 -3m^4-7m is a polynomial. A polynomial is an expression that can have constants, variables, and exponents, which are all combined using addition, subtraction, multiplication, and division, but never division by a variable. The given expression meets these criteria because it is composed of terms that are either constants or powers of m with coefficients, all added or subtracted together.

The degree of a polynomial is the highest power of the variable that appears in the polynomial. In the expression 5m^3 -3m^4-7m, the highest exponent attached to m is 4, so the polynomial is of the 4th degree. Polynomials are also categorized by the number of terms they contain. This polynomial has three terms, which makes it a trinomial.

In summary, 5m^3 -3m^4-7m is a trinomial of the 4th degree.