Squares and Cubes
Two common factoring situations involve (1) the difference between two squares, and (2) the sum or difference of two cubes.
Algebra
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Factoring
The process of factoring a real number involves expressing the number as a product of prime factors. Because a prime number has only two factors, the number 1 and the prime number itself, they are considered to be irreducible factors.
Solution of Equations and Inequalities
The solution of equations and inequalities involves finding the value (or values) of the variable(s) that make the mathematical statements true.
Inequalities
An algebraic inequality is a mathematical statement comparing two unequal algebraic expressions.
Equations
An algebraic equation is a mathematical statement equating two algebraic expressions, i.e., it states that one algebraic expression is equal to another algebraic expression.
The following additive and multiplicative properties apply to equations.
Polynomials
A monomial is a term containing variables with only nonnegative integers as exponents. The degree of a monomial is the sum of the exponents of its variables. The finite sum (or difference) of a set of monomials is known as a polynomial.
Algebraic Expression
A variable is a symbol that denotes a numerical quantity. Most variables are alphabetic characters. Algebra utilizes the concept of a variable to generalize mathematical concepts to a particular group of numbers, e.g. the set of real numbers. The number that the variable represents is called its value.
Set Notation
In the study of algebra, real numbers are often mentioned as a group, e.g. the set of real numbers greater than x, or the collection of real numbers satisfying a particular equation. Therefore, it is often convenient to indicate a particular group of real numbers using set notation.
Scientific Notation
A real number X expressed in scientific notation has the format
X = a × 10k, where 1 £ |a| < 10 and k is an integer
Notation
A real number can be represented in different ways. As mentioned before, a rational number (which is also a real number) can be expressed as an integer, as a quotient of two integers, and thus as a fraction (two integers separated by a "/"), or as a terminating or repeating decimal.
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