Lesson: Combining Factoring Techniques

Comment on Combining Factoring Techniques

Hi. I noticed that there is a lot of practice with difference of squares. Do you know of any sources that can provide practice with the other two special products?

Thank you!!

f a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3

Hi Brent,

Grateful for your solution for the above mentioned question please.
Thanks a lot
gmat-admin's picture

Nice question! I've now added it to the Reinforcement Activities.

Here's my full solution: https://gmatclub.com/forum/if-a-b-and-c-are-constants-a-b-c-and-x-3-x-x-...


C = -1
gmat-admin's picture

Yes, that's correct.

Could you please explain an easier way of tackling question 318 from OG19? It is a sum of cubes question so I was a bit surprised as I thought this was out of scope of GMAT? Anyways, question below for easy reference:

If xy =/ 0, is x^3 + y^3 > 0?
1. x + y > 0
2. xy > 0
gmat-admin's picture

Tricky question!
Here's my full solution: https://gmatclub.com/forum/if-xy-0-is-x-3-y-268848-20.html#p2637435

By the way, FACTORING sums of cubes is beyond the scope of the GMAT. However, for this question, we need not factor x³ + y³.


so I'm not sure but lowered choices that unit digit is 3.

here is what I do, so 15(15+54) unit digit is 5, (27-22)^2 unit digit is 5, add up to 0 and 63(-63+44) unit digit is -7 so that's why I narrowed down to 33% chances.
gmat-admin's picture

Question link: https://gmatclub.com/forum/15-310016.html

Perfect! As you can see, the question is super difficult. In such cases, student's must be on the lookout to maximize their odds of answering correctly. That's exactly what you did.
Nice work!

Sorry, I made a mistake here though the unit digit is the same, 27^2 - 22^2 IS NOT (27-22)^2, I think I have to clarify here...

Tweet about the course!

If you're enjoying this GMAT video course, help spread the word on Twitter.

Have a question about this video?

Post your question in the Comment section below, and a GMAT expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Free “Question of the Day” emails!