Solving by Factoring
Set the quadratic to 0, factor, then use the zero product property.
About this topic
To solve a quadratic equation by factoring, move everything to one side so the equation equals zero, factor the expression, then apply the Zero Product Property: if a product is zero, at least one factor must be zero. Set each factor equal to zero and solve.
For x² − 5x + 6 = 0, factor to (x − 2)(x − 3) = 0, so x = 2 or x = 3. These solutions are the x-intercepts, or roots, of the parabola. For an equation like x² = 7x, do not divide by x, which would lose the solution x = 0; instead write x² − 7x = 0 and factor x(x − 7) = 0.
Factoring is the fastest method when numbers are friendly, and it is used to find break-even points, dimensions of a rectangle with known area, and times when an object reaches a certain height.
The key mistake is trying to use the zero product idea when the right side is not zero. For (x − 2)(x − 3) = 12, you cannot set each factor equal to 12. Expand first, move 12 over, and refactor. Always check your answers in the original equation, and remember there can be two solutions, one repeated solution, or none real.
Key ideas
- Move everything to one side
- Each factor equals zero
- Roots are x-intercepts
Quick check
Use cases: where Solving by Factoring helps
- Homework: review the key idea behind Solving by Factoring before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Solving by Factoring without notes.
- Visual learning: play with the interactive lab to see how Solving by Factoring changes when you adjust its inputs.
- Teaching a friend: explain Solving by Factoring 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 Solving by Factoring?
Set the quadratic to 0, factor, then use the zero product property.
What will I learn in Solving by Factoring?
Move everything to one side. Each factor equals zero. Roots are x-intercepts.
Is Solving by Factoring 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 Solving by Factoring 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 Solving by Factoring?
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.