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Factoring Quadratics

Overview

Un-multiplying.

What is it?

Breaking x² + 5x + 6 into (x+2)(x+3).

History

The key to finding where a projectile hits the ground.

Key Idea

Find two numbers that multiply to C and add to B.

Practice This Topic

Concept Guide

Plain English: Factoring is figuring out what two things were multiplied to get this mess. It's math detective work.

Real-world example: Physics. Calculating how long a ball stays in the air.

How to do it

  1. Look at x² + bx + c.
  2. Find factors of 'c'.
  3. Find which pair adds up to 'b'.
  4. Write (x + ?)(x + ?).
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Common Pitfall

Mixing up the signs. Check if the middle number is positive or negative.

Word Problem
"A rectangle area is x² + 5x + 6. What are the sides?"
Reasoning: Factors of 6 that add to 5 are 2 and 3. Sides are (x+2) and (x+3).

Practice Examples

Diamond Method
x² + 7x + 12 (x + 3)(x + 4)
3x4=12, 3+4=7.