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Shared Factors – A Quadratics Puzzle

I shared this shared factors puzzle on twitter recently, but I thought I should share it on my blog as well.

Shared Factors Puzzle

Each side of the square shares a factor with each of its neighboring sides. Determine the missing values that make this statement true.

Shared Factors - A Quadratics Puzzle

This would be a great task for including in a polynomials or quadratics unit. I look forward to seeing how others incorporate it into their classrooms.

Adaptation by John Golden

John Golden brilliantly suggested that this problem could be reframed using an area model. I love the box method for polynomials, so I found this approach to be really satisfying.

If you like this approach, check out John Golden’s Geogebra adaptation.

Puzzle Solutions

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.

More Activities for Teaching Polynomials


Thursday 25th of November 2021

Could you explain how this works please. Explain the answer

Sarah Carter

Monday 29th of November 2021

Sorry, I do not share answers with students.