Solve Quadratic Equations by Factoring

Algebra-2

1. Fundamental Concepts

Definition: A quadratic equation is an equation of the form , where , , and are constants, and .
Factoring: Factoring a quadratic equation involves expressing it as a product of two binomials, , where and are constants.
Zero Product Property: If the product of two factors is zero, then at least one of the factors must be zero. This property is used to solve factored quadratic equations.

2. Key Concepts

Standard Form:

Factored Form:

Solution Method: Set each factor equal to zero and solve for .

3. Examples

Example 1 (Basic)

Problem: Solve by factoring.

Step-by-Step Solution:

Factor the quadratic expression:
Set each factor equal to zero:

Validation: Substitute and into the original equation:

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Example 2 (Intermediate)

Problem: Solve by factoring.

Step-by-Step Solution:

Factor the quadratic expression:
Set each factor equal to zero:

Validation: Substitute and into the original equation:

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4. Problem-Solving Techniques

Identify Coefficients: Clearly identify the values of , , and in the standard form .
Find Factors: Look for pairs of numbers that multiply to and add to .
Check Solutions: Always verify the solutions by substituting them back into the original equation.
Use Visual Aids: Draw a table or use a factor tree to help find the correct pair of factors.