Quadratic Equations by Factoring
Set to zero, factor, use the zero-product property.
Key idea
Set to zero, factor, use the zero-product property.
In depth
Write the equation as ax² + bx + c = 0, factor it, and use the zero product property: if AB = 0, then A = 0 or B = 0. This works because you cannot multiply two non-zero numbers to get zero.
Worked example
x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0 → x = 2 or x = 3.
Formula
Real-world uses
- Finding when a ball lands or when a rectangle has a given area and perimeter
Common mistake
Setting the product equal to a non-zero number and then splitting. Move everything to one side first.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quadratic Equations by Factoring?
Set to zero, factor, use the zero-product property. It is a topic at the intermediate level in Algebra.
What is the formula for Quadratic Equations by Factoring?
The key formula is ab = 0 ⇒ a=0 or b=0.
Where is Quadratic Equations by Factoring used in real life?
Real-world examples: Finding when a ball lands or when a rectangle has a given area and perimeter.
What should I learn before Quadratic Equations by Factoring?
Make sure you are comfortable with Sum and Difference of Cubes, the previous topic in Algebra.
What is a common mistake with Quadratic Equations by Factoring?
Setting the product equal to a non-zero number and then splitting. Move everything to one side first.
How can I practise Quadratic Equations by Factoring?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quadratic Equations by Factoring?
Move on to Completing the Square next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.