Quandaries and Queries


I am a student in 8th grade and i am taking a 10th grade level course (geometry) this upcoming year and they gave us a summer packet but i am having a little trouble answering some of the questions.

1) Can 4x2 + 19x + 12 be factored? i have tried but i cannot figure it out. Is there a way to find out if it cannot be factored before i try to work out the problem?

If you can find anyway to help that would be great.



Hi Nicole,

There really isn't a way to effectively determine if such an expression can be factored without trying all the possibilities. For this problem there are some clues that will help.

All the terms are positive so I know that if it factors then the factors will be of the form ax + b where a and b are positive.

The number 4 can be factored as 1 4 or 2 2 so, if the expression can be factored then I will have
4x2 + 19x + 12 = (x + ?)(4x + ??) or
4x2 + 19x + 12 = (2x + ?)(2x + ??).

At this point you need to try all possible integer choices for ? and ?? where ? ?? = 12 and see if you can get the "x-term" to be 19x. This is not all that hard as ? and ?? can only be 1 and 12, 12 and 1, 6 and 2, 2 and 6, 3 and 4, or 4 and 3.



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