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Mathematics: Working With Monomials and Polynomials

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Evaluating Polynomials

You can evaluate polynomials just as you have been evaluating expressions all along. To evaluate an expression for a value of the variable, you substitute the value for the variable every time it appears. Then use the order of operations to find the resulting value for the expression.

 

Working With Monomials and Polynomials

A monomial is an algebraic expression that has only one term.The basic building block of a polynomial is a monomial. A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the coefficient.

The coefficient can be any real number, including 0. The exponent of the variable must be a whole number—0, 1, 2, 3, and so on. A monomial cannot have a variable in the denominator or a negative exponent.

The value of the exponent is the degree of the monomial. Remember that a variable that appears to have no exponent really has an exponent of 1. And a monomial with no variable has a degree of 0. (Since x0 has the value of 1 if x ≠ 0, a number such as 3 could also be written 3x0, if x ≠ 0. as 3x0 = 3 • 1 = 3.)

A polynomial is an algebraic expression that has more than one term.