What Is A Term In A Polynomial?

The terms of a polynomial are the parts of a polynomial that are added to each other to form the polynomial. Each of these parts (terms) comprise a variable (or variables) raised to a given positive, whole-numbered power and a constant.

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The word "polynomial" is derived from the Greek word "poly," which means "many," and the Latin word "nomen," which means "name" or "terms." Thus, a polynomial is formed by adding many algebraic expressions together. Each algebraic expression consists of at least one variable raised to a given positive, whole-numbered exponent and a constant.

The general form of a polynomial is `a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + a_{n-3}x^{n-3} + \ldots + a_{2}x^{2} + a_{1}x + a_{0}` , where, `a_{n}, a_{n-1}, a_{n-2}, \ldots a_{2}, a_{1}, a_{0}` are real numbers, and n is a positive, whole number.

The terms of a polynomial are the algebraic expressions that are added to each other. Each term comprises a variable (or variables) raised to a positive whole-numbered exponent and a constant. In the above example, the first term of the polynomial, when the polynomial is arranged in descending order, is `a_{n}x^{n}` , the second term is `a_{n-1}x^{n-1}` , the third term is `a_{n-2}x^{n-2}` , . . ., and the last term is `a_{0}` .

The first term of the polynomial, when it is written in descending order is also called the leading term. It has the highest power of the variable. The coefficient of the leading term is called the leading coefficient, and the exponent of the variable in the leading term (in other words, the highest power) is the degree of the polynomial. In the above example, the leading term is `a_{n}x^{n}` , the leading coefficient is `a_{n}` , and the degree of the polynomial is n.

The last term of the polynomial given above is a constant. It does not contain a variable, only the coefficient `a_{0}` .

Example: Find the degree, leading term, leading coefficient, and constant of the following polynomial: `f(x) = 4x^{5} - 3x^{2} + 3`

The degree of the polynomial is 5.

The leading term is `4x^{5}`.

The leading coefficient is 4.

The constant is 3.

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