Factoring Trinomials
Find two numbers that multiply to c and add to b.
About this topic
To factor a trinomial x² + bx + c, find two numbers that multiply to c and add to b. For x² + 7x + 12, the numbers 3 and 4 work, so it factors as (x + 3)(x + 4). When the leading coefficient is not 1, use the "ac" method or trial and error.
Signs help: if c is positive the two numbers have the same sign as b, and if c is negative they have opposite signs. For x² − x − 6, you need a product of −6 and a sum of −1, so −3 and 2 work, giving (x − 3)(x + 2). For 2x² + 7x + 3, multiply a and c to get 6, find 1 and 6 that add to 7, split the middle term as 2x² + x + 6x + 3, and factor by grouping to get (2x + 1)(x + 3).
Factoring trinomials is how quadratics are solved without a formula and how rational expressions are simplified. Engineers factor to find when a projectile hits the ground.
Always take out a GCF first, and check by multiplying with FOIL. Not every trinomial factors with integers; if no pair works, the polynomial is prime over the integers and you will need the quadratic formula.
Key ideas
- For x² + bx + c look for factor pairs of c
- Signs depend on b and c
- Check with FOIL
Quick check
Use cases: where Factoring Trinomials helps
- Homework: review the key idea behind Factoring Trinomials before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Factoring Trinomials without notes.
- Visual learning: play with the interactive lab to see how Factoring Trinomials changes when you adjust its inputs.
- Teaching a friend: explain Factoring Trinomials in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Factoring Trinomials?
Find two numbers that multiply to c and add to b.
What will I learn in Factoring Trinomials?
For x² + bx + c look for factor pairs of c. Signs depend on b and c. Check with FOIL.
Is Factoring Trinomials part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Factoring Trinomials lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Factoring Trinomials?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.