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,
Gladi
“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)