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# I need help Factoring

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Intern
Joined: 14 Jan 2019
Posts: 1

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14 Jan 2019, 05:23
Hello Everyone,

I understand factoring and the theory behind it. However, I have issues coming up with the factorisations myself. Once I see an answer i can work towards it, but doing it myself is impossible. I don't know what the steps are that people take. In the official GMAT guide for example this problem is shown:

Step 1: 3x2 −3=8x
Step 2: 3x2 −8x−3=0
Step 3: (3x + 1)(x − 3) = 0
Step 4: 3x + 1 = 0 or x − 3 = 0
Step 5: x = − 13 o r x = 3

I understand how they go from step 2 to 3, but I would never be able to think of that myself. is there an easy way of coming up with this?
Math Expert
Joined: 02 Sep 2009
Posts: 58390
Re: I need help Factoring  [#permalink]

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14 Jan 2019, 05:53
kayduit wrote:
Hello Everyone,

I understand factoring and the theory behind it. However, I have issues coming up with the factorisations myself. Once I see an answer i can work towards it, but doing it myself is impossible. I don't know what the steps are that people take. In the official GMAT guide for example this problem is shown:

Step 1: 3x2 −3=8x
Step 2: 3x2 −8x−3=0
Step 3: (3x + 1)(x − 3) = 0
Step 4: 3x + 1 = 0 or x − 3 = 0
Step 5: x = − 13 o r x = 3

I understand how they go from step 2 to 3, but I would never be able to think of that myself. is there an easy way of coming up with this?

7. Algebra

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Senior Manager
Joined: 12 Jan 2019
Posts: 263
Re: I need help Factoring  [#permalink]

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14 Jan 2019, 05:57
kayduit wrote:
Hello Everyone,

I understand factoring and the theory behind it. However, I have issues coming up with the factorisations myself. Once I see an answer i can work towards it, but doing it myself is impossible. I don't know what the steps are that people take. In the official GMAT guide for example this problem is shown:

Step 1: 3x2 −3=8x
Step 2: 3x2 −8x−3=0
Step 3: (3x + 1)(x − 3) = 0
Step 4: 3x + 1 = 0 or x − 3 = 0
Step 5: x = − 13 o r x = 3

I understand how they go from step 2 to 3, but I would never be able to think of that myself. is there an easy way of coming up with this?

Don't worry if you're unable to factories it that way.
Fortunately, we have an alternative and better approach for Quadratic equations of form ax²+bx+c=0

Use Quadratic formula to get roots directly.
Formula is ;

X = [-b±(b²-4ac)^½]/2a

Even if you want to factories only, than also you can use this formula. For example, if you get x=1,2 with this formula, then the factors will be (x-1)(x-2).

You can use this formula in other situations too.

Posted from my mobile device
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In case my post helps you, please provide me with kudos. Thank you
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: I need help Factoring  [#permalink]

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14 Jan 2019, 06:40
1
Hi kayduit, Welcome to GMAT Club!

Quadratic factorization is fairly challenging for most people who are not from a math-heavy background. But a bunch of practice helps and I can assure you that you will only get better with every problem you solve. I have dave13 who could back up my claim as he as witnessed such an improvement first-hand

Now, let's take a look at the example you have quoted. I'll add my comments so you can get an idea of what goes through the mind of an advanced test taker.

$$3x^2 −3=8x$$ ...Okay, so this is a quadratic equation, need to get everything on one side so as to bring it into standard form
$$3x^2 −8x−3=0$$ ...Product of the roots is -3/3 = -1 and sum of the roots is 8/3 ( this is standard formula), so I need to find two numbers a & b such that ab = -9 and sum is -8 ... this comes out to be -9 and 1...
$$3x^2 -9x + x - 3 = 0$$ ... (Using the previous thinking -> -9x + x = -8x)
$$3x(x - 3)+1(x -3) = 0$$ ...Now (x-3) is common
$$(3x + 1)(x − 3) = 0$$ Taking the common factor out and finidng two clean product - that's it, factorization is complete
$$3x + 1 = 0$$ or $$x − 3 = 0$$
$$x = − 13$$ or $$x = 3$$

Remember, for successful algebraic factorization it is important that you split the middle term correctly. Feel free to tag or send a PM if you have follow-up questions.

Happy learning!
kayduit wrote:
Hello Everyone,

I understand factoring and the theory behind it. However, I have issues coming up with the factorisations myself. Once I see an answer i can work towards it, but doing it myself is impossible. I don't know what the steps are that people take. In the official GMAT guide for example this problem is shown:

Step 1: 3x2 −3=8x
Step 2: 3x2 −8x−3=0
Step 3: (3x + 1)(x − 3) = 0
Step 4: 3x + 1 = 0 or x − 3 = 0
Step 5: x = − 13 o r x = 3

I understand how they go from step 2 to 3, but I would never be able to think of that myself. is there an easy way of coming up with this?

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Re: I need help Factoring   [#permalink] 14 Jan 2019, 06:40
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