For my CAT this week I asked the student…

For my CAT this week I asked the students to answer the following question:

In which of the following three cases is the variable ‘a’ a factor?

1) abc
2) a + b + c
3) ab + c

Some of the answers I received were…

– In all three cases because ‘a’ is being multiplied/added and represents something.

– 1 and 3 because ‘a’ is being multiplied by something.

– 2 because ‘a’ is by itself and divides by itself.

This led to a good discussion where the conclusion was “something is a factor only if it is being multiplied by everything else in the expression”.

This idea of what a factor is can be hard to pin down. By the above definition someone might say in a(b + c) ‘a’ is not a factor because it is not being multiplied by ‘b’ and ‘c’. I hope this discussion helped alleviate some confusion.

If anyone tries this question in their class let me know what answers/conclusions are drawn.