Foundations

Standard Form

Each term in a polynomial has a degree. The term with the largest degree determines the degree of the polynomial. In order for a polynomial to be in standard form, the term with the largest degree must be listed first followed by the remaining terms in descending order of degree.

The following polynomials are in standard form:

4x4 - 3x3 + 2x2 - x +1

a4b3 - 2a3b3 + 3a4b - 5ab2 +2


The first term of a polynomial in standard form is called the leading term and the coefficient of the leading term is called the leading coefficient.

The first polynomial above has a leading term of 4x4 and a leading coefficient of 4.

The second polynomial above has a leading term of a4b3 and a leading coefficient of 1.