The Handy Math Answer Book

3. To obtain x,determine the solution for e^11 , or xis approximately 59,874.14172.


4. And finally, check your answer (using tables or your calculator) in the original
   equation ln(x) 11: ln(59,874.14172) 11 is definitely true.

POLYNOMIAL EQUATIONS

What is a polynomial?

In its simplest form, a polynomial is a mathematical equation that involves a sum of

powers in one or more variable, all of which is multiplied by coefficients. In such equa-

tions, variables and numbers on both sides of the equal sign are considered polynomi-

als. For example, by expanding out the expression (x2)^3 (or multiplying out the equa-

tion) we discover that (x2)^3 x^3  6 x^2  12 x8, which is a polynomial equation.

Are there other waysof describing polynomials?

Yes, there are other ways to describe polynomials. In particular, a polynomial with

only one variable is called a univeriate polynomial. A multivariate polynomialis one

with more than one variable.

There are other terms to further define polynomials, including the following:

Monomial—A monomial is a one-term polynomial (monomeans “one”). For

example, 3xis monomial.

Binomial—A binomial is a two-term polynomial (bimeans “two”). For example,

3 x^2 10 is a binomial.

Trinomial—A trinomial is a three-term polynomial (trimeans “three”). For exam-

ple, 4x^3  3 x6 is a trinomial.

What is the degreeof a polynomial equation?

The highest order power (or exponent) used in a univariate polynomial is called its

polynomial degreeor order;it is also defined as the largest (or maximum) sum of

exponents that appear on the variables in the equation’s terms. Commonly, the word

“degree” is used more frequently because “order” has another meaning when dis-

cussing polynomials.

You can also talk about degrees in reference to monomials, binomials, and trino-
mials. The degree of a monomial is the sum of the degrees of the variable in the equa-
tion; the degrees of the other polynomial equations are the greatest of the degrees in
terms after the equation has been simplified. For example, a third degree trinomial
150 equation is x^3 ^3 x^2 0.