Overview
This topic reviews the core algebraic skills needed for success in precalculus and calculus. These include manipulating expressions, solving equations and inequalities, and working with key algebraic properties and notation.
Key Concepts and Techniques
- Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)
- Combining Like Terms: Simplify expressions by grouping terms with the same variable and exponent.
- Factoring: Techniques such as GCF, difference of squares, trinomials, and grouping.
- Solving Equations: Solve linear and quadratic equations using inverse operations, factoring, and the quadratic formula.
- Inequalities: Solve linear and absolute value inequalities and graph their solutions on a number line.
- Distributive Property:
a(b + c) = ab + ac
- Zero Product Property: If
ab = 0, then a = 0 or b = 0
- Properties of Real Numbers: Commutative, associative, identity, inverse, and distributive properties.
Step-by-Step Example
Problem: Solve the quadratic equation: x^2 - 5x + 6 = 0
Step 1: Factor the quadratic expression.
x^2 - 5x + 6 = (x - 2)(x - 3)
Step 2: Apply the zero product property.
Set each factor equal to zero: x - 2 = 0 or x - 3 = 0
Step 3: Solve each equation.
x = 2 or x = 3
Answer: x = 2 or x = 3
Quick Tip
Always try factoring first when solving quadratic equations. It's faster than using the quadratic formula—and it gives you insight into the structure of the expression.