This document provides an overview of topics covered in Chapter 2 on quadratic equations and inequalities, including the factoring method, completing the square method, the quadratic formula, equations that lead to quadratics, applications, and quadratic and rational inequalities. It specifically discusses using the zero-factor property and a four-step process for solving quadratic equations by factoring the left side of the equation into two binomial factors and setting each factor equal to zero.

1. CHAPTER 2
Quadratic
Equations and
Inequalities

2. TOPICS:
• THE FACTORING METHOD
• The Square Root Property and the Method of
Completing the Square
• The quadratic Formula and the Discriminant
• Equations That Lead to Quadratic Equations
• Applications of Quadratic Equations
• Quadratic and Rational Inequalities

3. The Factoring Method
Quadratic Equation in x is an equation
that can be written in the standard form
𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎
Where a, b, and c are real numbers with a ≠ 0.

5. The Factoring Method
Zero-Factor Property
Let u and v represent real numbers, variables, or
algebraic expressions. If
𝒖𝒗 = 𝟎
Then, 𝒖 = 𝟎 𝒐𝒓 𝒗 = 𝟎. This property applies to
three or more factors as well.

7. MATH BOX
 Solving Quadratic Equations by Factoring
1. Write the equation in standard form, with the right
member zero.
2. Factor the left member of the equation.
3. Set each factor equal to zero.
4. Solve the resulting first-degree equations.
5. Check if the answers are correct by substituting them to
the variable in the original equation.