MGMAT Guide (Inequalties, VICS, etc.)

[Guest]

Hi,

Can you please solve the following equation? It's on Page 97 of the "Inequaties Guide." It's problem # 8. I know how to solve it using numbers (pretty easy), but would like to get some direction on how to solve it as is (i.e., for example, splitting it into a second-order equation and factoring).

Thanks for your help,
Guest

Problem (MGMAT Inequalities Guide, page 97, # 8)

(x^3 - 6x^2 - x + 30)/ (x-5) .......x not equal to 5.

[RonPurewal]

that polynomial doesn't factor by the traditional method for factoring four-term cubic polynomials (i.e., factoring by grouping the terms into 2 groups of 2 terms each with a common factor). if you want to do the division the 'textbook' way, you have to use one of two techniques:
- polynomial long division
- synthetic division
if you're curious, you can find details about either of these techniques in any algebra 2 textbook. i won't go into them here, because neither is essential content for the gmat.

BUT

the main point of this problem is to GET YOU PLUGGING IN NUMBERS. you said it yourself: plugging in numbers is 'pretty easy'. so that's what you should do!
this test is about time management as much as, or more than, content; therefore, if you have an easy and reliable method for solving a particular problem type, you should stick with it.