# Polynomial Operations and Theorems

## Vocabulary

### binomial

polynomial expression consisting of two terms

### complex zero

zero, where $a$ and $b$ are real numbers and $i=\sqrt{-1}$, written in the form:
$a + bi$

### degree of a polynomial

greatest degree of a term in a polynomial

### degree of a term

exponent of the variable of a term in a polynomial in one variable

### factoring

process of writing a number or algebraic expression as a product

coefficient of the first term of a polynomial written in standard form, which places the term with the highest degree first

### like terms

terms that have the same variable (or variables) with the same exponents

### monomial

polynomial expression consisting of one term

### polynomial function

function whose rule is a polynomial in one variable, which is a sum or difference of terms of the form $ax^n$, where $a$ is a real number and $n$ is a nonnegative integer

### polynomial in one variable

sum or difference of terms of the form $ax^n$, where $a$ is a real number and $n$ is a nonnegative integer

### synthetic division

process of long division of polynomials where only the coefficients and constants are recorded. The divisor must be a linear factor with a coefficient of 1.

### trinomial

polynomial expression consisting of three terms

### zero of a function

any input value of a function that makes the output of the function equal zero