Factoring Trinomials
Find two numbers that multiply to c and add to b.
Key idea
Find two numbers that multiply to c and add to b.
In depth
For x² + bx + c, find two numbers that multiply to c and add to b. For ax² + bx + c, use the ac method: find a pair that multiplies to ac and adds to b, split the middle term, then group.
Worked example
x² + 7x + 12: numbers 3 and 4 → (x + 3)(x + 4).
Formula
Real-world uses
- Solving projectile height questions and finding break-even points in business models
Common mistake
Getting the signs wrong when c is negative; one number must be negative.
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 Factoring Trinomials?
Find two numbers that multiply to c and add to b. It is a topic at the intermediate level in Algebra.
What is the formula for Factoring Trinomials?
The key formula is x²+bx+c = (x+p)(x+q).
Where is Factoring Trinomials used in real life?
Real-world examples: Solving projectile height questions and finding break-even points in business models.
What should I learn before Factoring Trinomials?
Make sure you are comfortable with Factoring Out the GCF, the previous topic in Algebra.
What is a common mistake with Factoring Trinomials?
Getting the signs wrong when c is negative; one number must be negative.
How can I practise Factoring Trinomials?
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 Factoring Trinomials?
Move on to Factoring by Grouping 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”.