1: Algebra Essentials


• 1.1: Real Numbers - Algebra Essentials
In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
• 1.2: Exponents and Scientific Notation
Mathematicians, scientists, and economists commonly encounter very large and very small numbers. But it may not be obvious how common such figures are in everyday life.
• 1.3: Radicals and Rational Expressions
The principal square root of a is written as √a. The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression.
• 1.4: Polynomials
In this section, we will examine polynomials, which are sums of or differences of terms, each consisting of a variable raised to a nonnegative integer power.
• 1.5: Factoring Polynomials
The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem. Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term. Trinomials can be factored using a process called factoring by grouping. Perfect square trinomials and the difference of squares are special products and can be factored using equations.
• 1.6: Rational Expressions
The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator.
• 1.7: The Rectangular Coordinate Systems and Graphs
Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the $$x$$-axis and the vertical axis the $$y$$-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the $$x$$-axis and the $$y$$-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
• 1.8: Linear Equations in One Variable
A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form ax+b=0ax+b=0 and are solved using basic algebraic operations.