Question 2212: How do you like no how to like factor- like if you have 6x squared plus 13x plus 5 you know that 5 and 1 work and 2 and 3 and 3 and 2 and all but how do you no which set of numbers you use in your equation?
PLLLEEAASEEE help i have a test on thursday and i don't get this at all- thanks!
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website!  factorises to (x+3)(x+2). This is found by finding 2 numbers that multiply to give the 6 and also add to give the 5.
Note however, that the  term has a coefficent of 1, so this "look and see" method of factorisation is fairly easy.
Factorisation becomes more tricky when the term has a coefficient not equal to 1, like your example, so you just have to do more mental work, that is all :-D.
So look at  . The first thing is that the solution will hopefully be either (6x..)(x..) or (3x..)(2x..), since both of these versions give the answer  .
So, we have to try both, i am afraid...no easier way :-(
One thing to make it easier however is that the "c" value is 5...so that narrows its possibilities right down to 1x5 straightaway, so we have 4 possible answers:
1. (6x + 5)(x + 1) or
2. (6x + 1)(x + 5) or
3. (3x + 5)(2x + 1) or
4. (3x + 1)(2x + 5)
A quick mental check of multiplying out the brackets (just the x-term) gives...
1. 6x + 5x = 11 WRONG!
2. 30x + x = 31x WRONG!
3. 3x + 5x = 8x WRONG!
4. 15x + 2x = 17x WRONG!
So all 4 are wrong so either, we cannot factorise "easily" and will have to use the quadratic formula OR (and i guess this is true) you have copied the question incorrectly!
I say this, since 15x MINUS 2x would give 13x, so i think the equation should be  which will factorise to (3x - 1)(2x + 5).
Does that help?
jon.
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