High school · Mathematics · 20 minutes
Solve a Quadratic by Factoring
Factor a simple quadratic and use the zero-product property to find solutions.
High School Math Foundations · Lesson 2 · Starter collectionLearning objective
Factor a simple quadratic and use the zero-product property to find solutions.
Gather your materials
- Paper or notebook
- Pencil; a calculator for checking arithmetic when appropriate
The lesson time covers the core activity. Allow extra time for video viewing and extended discussion.
Common Core skill focus
HSA.REI.B.4.bStandard level: High school · Algebra
Solve factorable quadratic equations by using their factors.
Read the official standard ↗Factoring is one method in this broader standard; completing the square, the formula and complex roots are outside this starter lesson. Code and level checked 2026-11-04; selected skill coverage.
Teach it step by step
- Ask what the learner already knows. Introduce the objective and read the explanation together.
- Work through the example aloud. Pause for the learner to explain why each step or piece of evidence matters.
- Choose a video if useful, then connect it to the example. Let the learner complete the independent practice before checking the explained answers.
- Discuss the question below and finish with the exit check. Revisit the example if the reasoning is unclear.
Watch, notice, discuss
Video choices for this lesson
Preview a video, then choose what fits your learners. “Show to class” opens a larger view; use the player’s play and full-screen controls when you’re ready.
Teacher preview needed. Check the language, level and length before showing. YouTube may show ads or related videos.
How To Solve Quadratic Equations By Factoring - Algebra Introduction
By The Organic Chemistry Tutor
Use this explanation as an introduction, then pause to connect it to the worked example and discussion question.
Open on YouTube: How To Solve Quadratic Equations By Factoring - Algebra Introduction (opens a new tab) ↗Factoring Trinomials & Polynomials, Basic Introduction - Algebra
By The Organic Chemistry Tutor
Compare this alternate explanation with the lesson. Ask learners to show their reasoning after watching.
Open on YouTube: Factoring Trinomials & Polynomials, Basic Introduction - Algebra (opens a new tab) ↗Why does a product equal to zero let us solve for two possibilities? Check both roots.
An external player loads only after you choose Preview or Show to class. Playback connects to YouTube. Videos belong to their creators; availability and embedding can change.
Understand the idea
A quadratic equation includes a nonzero squared term and can be written ax² + bx + c = 0. Factoring rewrites an expression as a product. If a product equals zero, at least one factor must be zero. This zero-product property applies only when the product is set equal to zero. Always check solutions in the original equation and then consider contextual restrictions.
Worked example
Solve x² − 5x + 6 = 0. Two numbers with product 6 and sum −5 are −2 and −3. Thus (x − 2)(x − 3) = 0, giving x = 2 or x = 3. Check x = 2: 4 − 10 + 6 = 0. Check x = 3: 9 − 15 + 6 = 0. Both are algebraic solutions.
Try it yourself
- Solve x² − 7x + 12 = 0 by factoring.
- Solve x² + x − 6 = 0.
- Why can you not set each factor equal to zero in (x − 2)(x − 3) = 10?
Check your reasoning
- (x − 3)(x − 4) = 0, so x = 3 or 4.
- (x + 3)(x − 2) = 0, so x = −3 or 2.
- The zero-product property requires a product of zero. First rewrite the equation with zero on one side, then solve the resulting quadratic.
Make it work for your learner
For support, model the example one step at a time and ask the learner to explain each choice in their own words. Use a sketch, organizer or physical model where helpful. For a challenge, create a new example, test an alternative explanation or describe when the model would not apply.
Exit check
Factor a simple quadratic and use the zero-product property to find solutions. Explain your reasoning with a specific example before moving on.
Prepare · Discuss · Reflect
Use evidence in a conversation
Discussion question: Why does a product equal to zero let us solve for two possibilities? Check both roots.
- Before discussing, write a tentative answer with two details from the lesson’s passage, example or data. For a longer discussion, the teacher can add an age-appropriate source.
- In pairs, a group or a tutor–learner conversation, agree on roles: facilitator, evidence finder and note taker. Combine roles when needed and allow equal time to respond.
- Share evidence, ask a clarifying question and respond to a different interpretation. Explain which details support or challenge a claim.
- Paraphrase another person’s point. Write a final conclusion explaining what changed, what remains uncertain and what evidence you would seek next.
Teacher look-for: Accurate use of the example, reasons linked to evidence, thoughtful questions and a response to another viewpoint. A well-supported alternative answer is welcome.