Solution by Factorization

Master the art of solving quadratic equations through factorization with interactive animations!

Welcome to Factorization!

Learn to solve quadratic equations by breaking them
into factors and finding their roots

Understanding Roots

Root (α): A value that makes the equation equal to zero
aα² + bα + c = 0

A quadratic equation can have a maximum of 2 roots

Factorization helps us find these roots by splitting the equation into factors

Factorization Method

Step 1
Write in standard form: ax² + bx + c = 0
Step 2
Split the middle term: Find two numbers that multiply to ac and add to b
Step 3
Factor by grouping: Group terms and factor out common factors
Step 4
Apply zero product property: If (p)(q) = 0, then p = 0 or q = 0

Step-by-Step Factorization

Ready to solve: 2x² - 5x + 3 = 0
2x² - 5x + 3 = 0
Click "Start Animation" to begin the factorization process

Interactive Examples

2x² - 5x + 3 = 0
Method: Split -5x into -3x - 2x
(2x - 3)(x - 1) = 0
Roots: x = 3/2, x = 1

Real-Life Application: Prayer Hall

A prayer hall expansion creates the equation: 2x² + 55x = 0
Let's solve it using factorization!
Original equation: 2x² + 55x = 0
Factor out x: x(2x + 55) = 0
Apply zero product property: x = 0 or 2x + 55 = 0
Solutions: x = 0 or x = -27.5
In context: Only x = 0 makes physical sense
Choose a topic below to start learning about factorization!
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📊 Understanding Factorization
Factorization is a powerful method for solving quadratic equations by expressing them as products of linear factors. This approach reveals the roots directly and provides insight into the equation's structure and behavior.