Intermath | Workshop Support


The 26th Degree/FOIL Frenzy

Problem Statement
What is (x-a)(x-b)(x-c)...(x-y)(x-z)? Explain how you found the answer.

Problem setup

When I first looked at this problem I thought I would have to multiply 26 variables together.  After thinking about the problem and listening to class discussion I felt there must be a pattern that would help solve the problem.  I looked up the definition of a mathematical pattern and looked for regularity. 


Plans to Solve/Investigate the Problem

Problem solving strategies including reading the problem, recalling and discussing terminology and functions, using trial and error computations, making tables or charts, looking for a simpler problem and generalizing would be employed.  Definitions of unknown terminology were looked up on the Intermath dictionary.

Prior to beginning I looked up the definition of a mathematical pattern in the Intermath dictionary.  The definition of a mathematical pattern per the Intermath dictionaly is “a mathematical pattern involves regularity. This regularity may manifest itself in shape, direction, orientation, size, or number relationships, among other things. The key to being a pattern is that there is some regularity that can be repeated, extended, or built upon.”

Investigation/Exploration of the Problem

The problem was approached by brainstorming as a class.  Then individually and collectively, the class applied foil to the first terms (x-a) * (x-b).


Extensions of the Problem

What would the constant be in the final problem? 

Author & Contact
Susan R. Kelly

Link(s) to resources, references, lesson plans, and/or other materials
Link 1
Link 2


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