A combined developmental algebra textbook by Sherri Messersmith covering the full beginning + intermediate algebra sequence: real numbers, exponents, linear equations and inequalities, linear equations in two variables and functions, systems of linear equations, polynomials, factoring, rational expressions and equations, absolute value equations and inequalities, radicals and rational exponents, quadratic equations and functions, functions and their graphs, exponential and logarithmic functions, and conic sections. POWER refers to Messersmith's embedded Prepare-Organize-Work-Evaluate-Rethink learning framework. This is the developmental-algebra text adopted at College of DuPage.
Foundational pre-algebra/early algebra review: fractions, decimals and percents, the order of operations and exponents, sets of real numbers, and an introduction to algebraic notation.
Rules of exponents: product rule, quotient rule, power rules, zero exponent, and negative exponents. Scientific notation.
Solving linear equations in one variable, applications and word problems, equations with multiple variables, proportions and ratios, and linear and compound inequalities.
Introduction to graphing in two variables, slope of a line, equations of lines (slope-intercept, point-slope, and standard forms), and graphing linear inequalities in two variables.
Solving systems of linear equations by graphing, substitution, and elimination methods; applications of systems; systems with three equations.
Polynomial vocabulary and operations: addition, subtraction, multiplication, and division of polynomials.
Factoring techniques: GCF, grouping, trinomials with leading coefficient 1 and not 1, special forms (difference of squares, perfect-square trinomials, sum/difference of cubes), and solving quadratic equations by factoring.
Simplifying rational expressions; multiplying, dividing, adding, and subtracting rational expressions; complex fractions; solving rational equations; applications; and variation.
Solving equations and inequalities involving absolute value expressions.
Radicals, rational exponents, simplifying radicals, operations on radicals, rationalizing denominators, radical equations, and complex/imaginary numbers.
Methods for solving quadratic equations: factoring, completing the square, the quadratic formula, and the square-root property; equations quadratic in form; applications.
Function notation and definitions, graphing parent functions and their transformations, quadratic functions and their graphs, and applications of quadratic functions.
One-to-one functions and inverse functions, exponential functions, and logarithmic functions at a developmental-algebra level (introduction; properties of logs and complete exponential/log equation solving expand in college algebra).