Factor the expression.

Question

Factor the expression. 72x2 + 78x + 15

A. 3(6x - 5)(4x - 1)

B. 3(6x + 5)(4x + 1)

C. (72x + 1)(x + 15)

D. Prime Polynomial

Answer 1

Two things to note:

1. There is, believe it or not, a reason to learn how to factor.  Factoring is one of those math things you have to get "a feel for" and that only comes from doing it.  In this case you have 3 numbers to factor into the form (ax+b)(cx+d) the terms are all positive, which makes it simpler.  72 has a lot of possible factors 78 has fewer and 15 has only 1,3,5 and 15.  BUT all three are divisible by 3 so we can pull the three out giving us 3(24x^2+26x+5) which is somewhat simpler.  So now we need to look at the factors that when multiplied by each other equal 24 (the 'a' and 'c' terms above) and when multiplied by the other and summed equal 26, that is ad+bc=26.  Additionally bd must equal 5, but since the only factors of 5 are 1 and itself we know that b will either be 1 or 5 and that d will be whatever is left after picking b.  All together now we have:
1. (ax+5)(cx+1) and we need ac=24 and 5*c+1*a or vice versa to equal 26. 
2. So now it is time for you to play with the numbers!
2. I would point out that if this was a test and you were not having any factoring luck, you could either eliminate answers based on what you know or expand the answers until you got the original equation.  I would not recommend this for homework assignments, but when the pressure is on use whatever advantages you can.

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