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jmuduke08
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quick factoring question 05 Jan 2013, 14:41
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wasnt sure how to post this in quant section without having to list a specific problem but my question is...

is there a quick way to factor the equation: r^2-3r-180 = 0? I know the solution after trial and error but I was getting tripped up on two factors that multiply to get to 180 off the top of my head. given gmat problems are 2 min or less was hoping you guys might have an easy shortcut. Thanks!
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quick factoring question 05 Jan 2013, 16:46
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This might help you:- algebra-101576.html#p787276

for quick factorization ,you are looking for 2 numbers, whose multiplication gives you 180 and when added they give you -3. there is no such pair for this equation (that is because D<0 for this equation and hence no solution exists. go through the above link for an explanation)
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quick factoring question 05 Jan 2013, 16:52
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My apologies I meant to type r^2-3r-180=0. Which give the solutions 15 and -12. I just wanted to know the quick way to get these high digit factors. I know how to factor but in terms of quickness, I couldn't think of 15 and -12 without a ton of trial and error which took too long

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quick factoring question 05 Jan 2013, 23:08
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1. I don't think you need to factor anything here.
2. Speed comes with practice
3. I fixed the typo in your first post (changed the + sign to -)

This is a tough equation, definitely designed to slow you down since even using the Quadratic formula it will take some time and few know that 729 is a square root of 27...

Your best bet is to think what 2 numbers are factors of 180 (but I would not want to do that on the real test)... I think the Quadratic formula is the best way to go and looking at 729 (the 9 is a giveaway that it is either 3 or 7 that will be involved).
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quick factoring question 06 Jan 2013, 12:02
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jmuduke08
My apologies I meant to type r^2-3r-180=0. Which give the solutions 15 and -12. I just wanted to know the quick way to get these high digit factors. I know how to factor but in terms of quickness, I couldn't think of 15 and -12 without a ton of trial and error which took too long

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bb is right. Use the quadratic formula if it takes a lot of time to proceed by hit and trial.

for hit and trial:

I haven't yet seen any GMAT quadratic question in the form of ax^2+bx+c=0 with fractions/irrational numbers as roots . Almost always the solution will be integers. I'll write my thought process; see if that helps you quicken your hit and trial: (obviously this will look way longer than what happens in my head :) )

r^2-3r-180=0

this is what I make out of 180 and 3 at the first instant:
looking for 2 numbers whose product is 180 and sum is -3.
sum is negative -> implies bigger of the absolute factors is negative and the smaller is positive.

the second step is:
I break 180 into the simplest factors I can see. 18 x 10 in this case.
if it doesn't happen for me (as in this case) i break each into 2 more (simple) factors. (6x3)x(5x2)

this does it for me. I know 12 and 15 are the numbers I'm looking for. The key is not to break 180 into its prime factors but two simpler composite factors.

I don't know whether this helps or not. I just meant to show that you can work on your hit and trial (it should not take a ton of time). Saying that, if you don't have enough time for your GMAT, it would be wise to use the quadratic formula.

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