A variable is a letter that can represent any number from a given set of numbers. If we start with variables, such as x, y, and z, and some real numbers and combine them using addition, subtraction, multiplication, division, powers, and roots, we obtain an algebraic expression. Here are some examples:

2x2 - 3x + 4 + √x + 10

A monomial is an expression of the form axk, where a is a real number and k is a nonnegative integer. A binomial is a sum of two monomials and a trinomial is a sum of three monomials. In general, a sum of monomials is called a polynomial. For example, the first expression listed above is a polynomial, but the other two are not.

Note that the degree of a polynomial is the highest power of the variable that appears in the polynomial.

Adding and Subtracting Polynomials

Special Product Formulas

Factoring Common Factors

Factoring Trinomials

Factoring x 2 + bx + c by Trial and Error

Special Factoring Formulas

Recognizing Perfect Squares: