A polynomial in one variable is said to be in standard form when it is expressed as a sum of terms, where each term is a product of a constant coefficient and a variable raised to a non-negative integer exponent. The standard form is typically written in descending order of the exponents of the variable.
For example, a polynomial in standard form can be represented as:
p(x) = anxn + an-1xn-1 + … + a1x + a0
where:
- an, an-1, …, a1, a0 are constants from the set of real numbers (or complex numbers),
- x is the variable, and
- n is a non-negative integer that represents the degree of the polynomial.
This means that the highest degree term comes first, followed by the next highest, and so forth down to the constant term. For instance, the polynomial 3x4 – 5x2 + 2 is in standard form, while 2 – 5x2 + 3x4 is not, as the terms are not arranged in descending order of the variable’s exponent.