Polynomials are mathematical expressions with variables raised to non-negative integer powers.
They take the form of $a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0$ where $a_n,a_{n-1},\cdots ,a_1,a_0$ are coefficients.
The highest power of x is the degree of the polynomial.
Polynomials are essential in algebra and can be used to represent various mathematical relationships.

Division of polynomials is a process similar to long division with numbers, but it involves polynomials instead.
The goal is to divide a polynomial (the dividend) by another polynomial (the divisor) to obtain a quotient and possibly a remainder.
The process can be done using long division or synthetic division, depending on the divisor.

The Remainder Theorem is a useful concept in algebra, especially when dealing with polynomials.
It provides a quick way to find the remainder of the division of a polynomial by a linear binomial of the form $x-c$ without having to perform the actual polynomial division.

The Factor Theorem is closely related to the Remainder Theorem and is a powerful tool in polynomial algebra.
It provides a direct method for identifying factors of polynomials and, by extension, their roots.

The Rational Zero Theorem (or Rational Root Theorem) is a useful mathematical principle that helps identify all possible rational zeros (or roots) of a polynomial equation.
It's especially helpful when you're dealing with polynomials of higher degrees and looking for where to start with root-finding efforts.

Solving polynomial equations is a fundamental part of algebra that involves finding the values of the variable that make the equation true.
These values are known as the roots or zeros of the polynomial. There are several methods to solve polynomial equations, and the choice of method often depends on the degree of the polynomial and its specific form.

Polynomials are mathematical expressions involving a sum of powers in one or more variables multiplied by coefficients.
They play a crucial role in various areas of mathematics and its applications. The characteristics of polynomials can help us understand their behavior and how to work with them.

Graphing polynomials involves understanding their basic properties and characteristics, such as degree, roots (zeros), end behavior, and critical points.