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 4x^{2} + 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.
At this point you need to try all possible integer choices for ? and ?? where ? ?? = 12 and see if you can get the "xterm" 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. Penny 

