Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

GUYS, Any idea how to factor ? (i came across this in OG though have no idea how they factored it )

5x^2-34x+24

You can try this small trick: Add and substract the same numbers. This opperation does not change the value of the expression, but allows you to factor it:

GUYS, Any idea how to factor ? (i came across this in OG though have no idea how they factored it )

5x^2-34x+24

You can try this small trick: Add and substract the same numbers. This opperation does not change the value of the expression, but allows you to factor it:

the equation in the question that you have posted is a quadratic equation of the form ax^2 + bx + c where a is coefficient of x^2 term, b is coefficient of X term and C is the constant.

now ax^2+ bx + c can be factored into (x-r1)(x-r2)

where (r1,r2) = ((-b+sqrt(b^2-4ac)/2a),(-b-sqrt(b^2-4ac)/2a))

Trust it is a simple and important concept, please follow the link I pasted below. get back if you want further details!

GUYS, Any idea how to factor ? (i came across this in OG though have no idea how they factored it )

5x^2-34x+24

You can try this small trick: Add and substract the same numbers. This opperation does not change the value of the expression, but allows you to factor it:

Yes... The method quoted by Fluke may also be used

This is the general formula for roots of a quadratic equation. It will be helpful to remember that. Aslo, 1. if the term under the root is less than zero, the equation has no real solution 2. if the term is 0, the equation has only one solution 3. if the term is greater than zero, the equation has two real and distinct solution. _________________

"Wherever you go, go with all your heart" - Confucius

I was going to post this as an alternative, thank you for beating me to it. Although this method would take me about a minute and a half, it would be shorter than using the splitting method (I'm just not good at it). _________________

"Only by going too far, can one find out how far one can go."

I was going to post this as an alternative, thank you for beating me to it. Although this method would take me about a minute and a half, it would be shorter than using the splitting method (I'm just not good at it).

Actually you will almost never need to use the formula on GMAT. Whenever you have a quadratic that you need to factor, you will almost always get two integral roots (in GMAT). If I am looking at a GMAT question and am unable to find the factors, I will go back and check my quadratic to see if it is correct rather than try to use this formula... I would be that sure of not needing to use it!

And as for '(I'm just not good at it)', it is just about a little bit of practice. I assume you know that you need to find the factors that add up to give the middle term and multiply to give the product of the constant term and co-efficient of x^2. What you may have problems with is splitting the middle term.

e.g. the question above: \(5x^2-34x+24\) If you need to factorize it, you need find two numbers a and b such that:

a + b = -34

a*b = 5*24

Step 1: Prime factorize the product. a*b = 2*2*2*3*5

Step 2: Check the signs and decide what you need. Here sum is -ve while product is positive. This means a and b both are negative. Both will add to give a negative number and multiply to give a positive number. It also means that a and b both are smaller than 34 (since they will add up to give 34. If one of them were negative and other positive, one number would have been greater than 34. In that case, the product would have been negative.)

Step 3: Try to split the prime numbers into two groups such that their sum is 34. Try the most obvious group first i.e. 2*2*2 and 3*5 ---- 8 and 15 add up to give 23. But you need 34, i.e. a number greater than 23.

Before we discuss the next step, let me explain one thing: Let's say we have 2*2*5*5.. I split it into 2 groups 2*5 and 2*5 (10 and 10). Their sum is 20. I split in in another way 2*2 and 5*5 (4 and 25). Their sum is 29. The sum increased. I split in in another way 2 and 2*5*5 (2 and 50). Their sum is 52. The sum increased again.

Notice that farther apart the numbers are, the greater is their sum. We get the least sum (20) when the numbers are equal.

Going back to the original question, 8+15 gave us a sum of 23. We need 34 so we need to get the numbers farther from each other but not too far either. Let's say, I pick a 2 from 8 and give it to 15. I get two numbers 4 and 30. They are farther apart and their sum is 34. So the numbers we are looking for are -4 and -30 (to get -34 as sum)

Taking another example: \(8x^2 - 47x - 63\)

a + b = -47 a*b = 8*(-63) = - 2*2*2*3*3*7

One of a and b is negative since the product is negative. So one of a and b is greater than 47. I split the primes into two groups: 2*2*2 and 3*3*7 to get 8 and 63 but 63 - 8 = 55. We need to go lower than 55 so we need to get the numbers closer together. 63 is way greater than 8. Take off a 3 from 63 and give it to 8 to get 21 and 24. Too close. Rather take off 7 from 63 and give it to 8 to get 9 and 56. Now, 56 - 9 = 47 so you have your numbers as 56 and 9. The greater one has to be negative since the sum is negative so you split the middle term as: -56 and 9.

With a little bit of practice, the hardest questions can be easily solved... _________________

Hi Pardon me. I don't know if you mean "a + b = -34". Why? How is this method? Lets factors be = (5x - a) (x - b) = 5x^2 -34x + 24 a + 5b = 34 ab = 24 Hence a=4, b=6 (5x - 4)(x - 6) are the factors.

VeritasPrepKarishma wrote:

TwoThrones wrote:

I was going to post this as an alternative, thank you for beating me to it. Although this method would take me about a minute and a half, it would be shorter than using the splitting method (I'm just not good at it).

Actually you will almost never need to use the formula on GMAT. Whenever you have a quadratic that you need to factor, you will almost always get two integral roots (in GMAT). If I am looking at a GMAT question and am unable to find the factors, I will go back and check my quadratic to see if it is correct rather than try to use this formula... I would be that sure of not needing to use it!

And as for '(I'm just not good at it)', it is just about a little bit of practice. I assume you know that you need to find the factors that add up to give the middle term and multiply to give the product of the constant term and co-efficient of x^2. What you may have problems with is splitting the middle term.

e.g. the question above: \(5x^2-34x+24\) If you need to factorize it, you need find two numbers a and b such that:

a + b = -34

a*b = 5*24

Step 1: Prime factorize the product. a*b = 2*2*2*3*5

Step 2: Check the signs and decide what you need. Here sum is -ve while product is positive. This means a and b both are negative. Both will add to give a negative number and multiply to give a positive number. It also means that a and b both are smaller than 34 (since they will add up to give 34. If one of them were negative and other positive, one number would have been greater than 34. In that case, the product would have been negative.)

Step 3: Try to split the prime numbers into two groups such that their sum is 34. Try the most obvious group first i.e. 2*2*2 and 3*5 ---- 8 and 15 add up to give 23. But you need 34, i.e. a number greater than 23.

Before we discuss the next step, let me explain one thing: Let's say we have 2*2*5*5.. I split it into 2 groups 2*5 and 2*5 (10 and 10). Their sum is 20. I split in in another way 2*2 and 5*5 (4 and 25). Their sum is 29. The sum increased. I split in in another way 2 and 2*5*5 (2 and 50). Their sum is 52. The sum increased again.

Notice that farther apart the numbers are, the greater is their sum. We get the least sum (20) when the numbers are equal.

Going back to the original question, 8+15 gave us a sum of 23. We need 34 so we need to get the numbers farther from each other but not too far either. Let's say, I pick a 2 from 8 and give it to 15. I get two numbers 4 and 30. They are farther apart and their sum is 34. So the numbers we are looking for are -4 and -30 (to get -34 as sum)

Taking another example: \(8x^2 - 47x - 63\)

a + b = -47 a*b = 8*(-63) = - 2*2*2*3*3*7

One of a and b is negative since the product is negative. So one of a and b is greater than 47. I split the primes into two groups: 2*2*2 and 3*3*7 to get 8 and 63 but 63 - 8 = 55. We need to go lower than 55 so we need to get the numbers closer together. 63 is way greater than 8. Take off a 3 from 63 and give it to 8 to get 21 and 24. Too close. Rather take off 7 from 63 and give it to 8 to get 9 and 56. Now, 56 - 9 = 47 so you have your numbers as 56 and 9. The greater one has to be negative since the sum is negative so you split the middle term as: -56 and 9.

With a little bit of practice, the hardest questions can be easily solved...

Hi Pardon me. I don't know if you mean "a + b = -34". Why? How is this method? Lets factors be = (5x - a) (x - b) = 5x^2 -34x + 24 a + 5b = 34 ab = 24 Hence a=4, b=6 (5x - 4)(x - 6) are the factors.

There are many ways of arriving at the factors. One method is splitting the middle term: \(5x^2 -34x + 24 = 5x^2 -30x - 4x + 24 = 5x(x - 6) -4(x - 6) = (5x - 4)(x - 6)\)

or simply, when you split the middle term into 30 and 4, the factors are \(5x^2 -34x + 24 = 5(x - 30/5)(x - 4/5)\)

What you have done is fine too of course, though for most people, a + 5b = 34 is definitely more difficult to work with than a + b = 34. Hence, more often than not, I suggest splitting the middle term. Use whatever works for you. _________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...