Polynomials definition and examples.

Polynomials definition:

A polynomial is a sum of monomials.

A polynomial example:

2a + 5b

In the example, two terms are combined using addition.

Polynomials examples:

123abd + 2a + 3b + 4d

In the example, the four terms are combined using addition. All the terms are monomials.

456x^{2}y^{3}z^{4} + 12xyz

Here two monomials are combined using addition. The exponents of variables can only be whole numbers: 0; 1; 2; 3; 4;...

That is why expressions like this: 2x^{-3} cannot be polynomials, the exponent of the variable must be a whole number.

A single variable is a polynomial, too:

k

the "k" is a polynomial. But where is the addition here? Here the «k» can be replaced with: k + 0.

A single number is a polynomial, too. Examples:

1; 2; -12; 1/2

All the numbers are polynomials.

Is zero a polynomial? Yes, it is.

All monomials are simultaneously polynomials. Examples:

2k; 567abc; 4b^{2}

Is this expression a polynomial?

5x + 6/x

No, it is not a polynomial. Why? It is because in the second term the 6 is divided by x. Polynomials cannot have division by a variable.