Solving by Factoring and the Zero Product Property
I can solve a quadratic equation by getting 0 on one side, factoring and setting each factor to 0.
What students learn
Students learn to solve a quadratic equation by factoring: they move every term to one side so the other is 0, factor fully, set each factor equal to 0, and verify each solution in the original equation.
See inside
The key rule
Get 0 alone on one side first. Then set each factor with x equal to 0 and solve each one.
ab = 0 → a = 0 or b = 0
Write the solutions together with 'or', then check each in the original.
Watch out
To solve (x − 3)(x + 1) = 12, a student writes x − 3 = 12 or x + 1 = 12.
The mistake: x = 15 or x = 1112 is not 0: a product of 12 says nothing about either factor.
The fix: x² − 2x − 15 = 0, so x = 5 or x = −3Check x = 15: 12 · 16 = 192, not 12.
The mistakes it targets
- Sets each factor equal to a number that is not 0
- Reads the solutions' signs straight off the factors
- Counts a constant factor as giving a solution
- Drops the constant when moving every term to one side
- Factors with the signs swapped
- Divides both sides by x and loses the solution x = 0
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, six common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.