Which Algebraic Expression Is a Polynomial 3m2n 4m5 3mn5 7mn?

There are a few different algebraic expressions that could be considered a polynomial, but the most likely one is 3m2n 4m5 3mn5 7mn. This expression is a polynomial because it is a combination of terms that are all monomials or powers of monomials. Each term in the polynomial has a degree, which is the sum of the exponents of the variables in that term. The degree of the entire polynomial is the highest degree of any of its terms. In this case, the highest degree is 5, which is in the term 4m5.

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A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable raised to a non-negative integer power and multiplied by a coefficient. An example of a polynomial is x 2 + 5x + 6. The degree of a polynomial is the highest exponent of the variable in any of the terms. In the example above, the degree of the polynomial is 2. The coefficients of a polynomial can be any numbers, including zero and negatives.

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A polynomial is an expression consisting of a sum of terms, each term including a variable raised to a non-negative integer power and multiplied by a coefficient. The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, the leading coefficient of x3 + 2x2 + 5x + 1 is 1.

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In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1.

Polynomials appear in a wide variety of areas of mathematics and science. For instance, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from interpolation and approximation theory to solving differential equations; they are used in calculus and numerical analysis to approximate other functions. In linear algebra, polynomials can be used to construct polynomial vector spaces.

The term "polynomial" is derived from the Greek word πολύς (polús, "many"), and μονάς (monás, "one"). It was used by Apollonius of Perga and other ancient Greek mathematicians and is still used in modern Greek.

A polynomial in one indeterminate (variable), x, is a formula of the form:

a0 + a1x + a2x2 + ... + anxn

where the coefficients a0, a1, ..., an are real numbers, and n is a non-negative integer. The coefficients are often taken to be rational numbers, but they can also be taken to be arbitrary real or complex numbers. The degree of a polynomial is the largest exponent of the variable that appears in the formula, and the leading coefficient is the coefficient of the term of highest degree. If the degree is 0, the polynomial is the constant polynomial a0. The degree of a constant polynomial is 0.

The degree of a non-zero polynomial in one variable x is the highest exponent of x in the polynomial. The degree of the zero polynomial is undefined.

The leading term of a polynomial is the term of highest degree. The leading coefficient of a polynomial is the coefficient of the leading term.

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