Math Help Polynomials
July 6th, 2007
In this section of Math Help online, we discuss polynomials and polynomial equations.
What is a polynomial? What are polynomials? Definition of a polynomial
A polynomial in x, denoted by P(x), consists of one or more terms such that the terms are either
- an integral constant or
Examples of polynomials in x and equations that are not polynomials in x are shown below:
- 3 x3 + 2 x2 + 1 is a polynomial in x.
- 3 x3 + 2 x 1/2 + 1 is a not a polynomial in x. (This is because 1/2 is not an integral power of x.)
- 3 x3 + 2 x -2 + 1 is a not a polynomial in x. (This is because -2 is not a positive power of x.)
The degree of a monomial is the sum of the exponents of the variables.
Examples of degrees of a monomial are shown below:
- Monomial 3 x3 has degree of 3
This is because x has degree of 3, Y has degree of 2 and z has degree of 1, so the total degree of the monomial is 3+2+1 = 6.
- Monomial 5 has degree of zero
This is because there is no variable shown in the monomial. When there is no variable terms such as x or y shown in the monomial, the variable still exists but has the degree of zero. All variable with degree zero equal one. For example, the variable is x 0 which is equal to 1. In another word, monomial 5 in the example can be written as 5 x 0 .
Since x 0 = 1, 5 x 0 = 5 and there is no need to write x 0 out.
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