A. Polynomials
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A. Polynomials
A monomial is a special polynomial with a single term. The following are examples of monomials. Notice that each can be produced by multiplying numbers and variables with whole number exponents.
More complex polynomials can be produced by adding one or more monomials. For example, a two-term polynomial, or binomial, is produced by adding two monomials.
A three-term polynomial, or trinomial, can be produced by adding three monomials.
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Monomial
a single-term algebraic expression that is the product of numbers and variables with whole number exponents; the expressions 5x2 , 3 xy3 , and −7 are monomials Polynomial a sum of one or more monomials; −4x3 and x2 + 4x − 19 are polynomials Term a summand of a polynomial; the polynomial 3x2 + 12x − 7 includes the terms 3x2, 12x and −7 Coefficient the numerical part of a monomial; the coefficients of 4x , −x3 y2, and −5 are 4, −1, 1, and −5 , respectively Binomial a polynomial with two terms Trinomial a polynomial with three terms |
The following table shows some expressions that are not polynomials.
| Expressions | Reason it is not a polynomial |
|---|---|
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The variable in
 is inside a radical.
Written in exponential form,  The exponent is not a whole
number. |
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The variable in
is in the denominator.
Written in exponential form,  . The exponent is not a whole number.
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The variable in
 has a negative exponent.
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