Polynomials I

A polynomial is an algebraic expression made of real-number coefficients and variables, where the variables are raised to whole-number exponents.

We classify polynomials in two ways. One way is by the number of unlike terms they contain. A polynomial with one term is called a monomial, with two terms a binomial, and with three terms a trinomial.

The other way is by the highest exponent with a non-zero coefficient, called the degree.

For example, 3x cubed plus 2x squared plus 1 is a trinomial with a degree of 3. Here, the x raised to the power 1 term is missing, but the expression is still a polynomial.

Polynomials help in representing real-world situations. Consider a rectangular garden with a length of x meters and a width of x + 2 meters, with an area of x squared plus 2x, a polynomial. As x changes, this single expression can calculate the area for any-sized garden.

But not every algebraic expression is a polynomial. Expressions with negative or fractional exponents are not polynomials because those exponents are not whole numbers.