How should I approach this problem?

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kitsae

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(2x[sup:khsiwdgh]3[/sup:khsiwdgh]+5x[sup:khsiwdgh]2[/sup:khsiwdgh]-33x+20)/(2x-5)

(1) I set the problem up as follows:

(2x[sup:khsiwdgh]3[/sup:khsiwdgh]+5x[sup:khsiwdgh]2[/sup:khsiwdgh]-33x+20)
___________________________________
(2x-5)

(2) From here, I would suspect that the numerator would have to be simplified through factoring. However, I am only familiar with factoring simple quadratics (such as x[sup:khsiwdgh]2[/sup:khsiwdgh]+5x+6=(x+2)(x+3).

Question: I'm not sure how to factor such a complex numerator. Could you please help me set it up (i.e. how to properly factor the numerator) so that I can take a crack at solving the problem?
 
kitsae said:
How should I approach this problem?
Click to expand...


Since there are different methods to factor a cubic polynomial, you should approach this problem using the method taught in your class.

Have you learned about Descartes' Rule of Signs and the Rational Zeros Theorem?

How about polynomial division (longhand or synthetic)?

Either of these methods are easier than the others.

With the former method, the strategy is to find values of x that are zeros of the polynomial in the numerator.

Once you know that a number (I'll call it C) is a zero, then you know that (x - C) is a factor.

With the latter method, you guess that the denominator is probably a factor (because these exercises are cooked up to simplify nicely). You then use polynomial division to divide the numerator by the denominator. If it divides evenly, then the quotient is a factor.

The quotient will be a quadratic polynomial, which, if factorable, can be factored in the normal way.

 
I actually am not taking a class. I'm trying to self-teach myself the material without a textbook (which is proving insanely difficult). I'll read through the purple math forums to see if it provides me with the necessary background to tackle these problems.

I'm using problems out of this book: http://www.amazon.com/Schaums-Outline-C ... 0071402276

However, the book provides absolutely no explanatory material. Being an outline, it assumes that you've already learned the material. Unfortunately, the last time I learned the material was about a decade ago.

Any on-line or text resources that you can provide me would be a great help.

Lastly, my motive for re-learning this material is to eventually take the GMAT.
 
By the way - performed polynomial long division (as suggested) and obtained the correct answer. Thank you!
 
I'm having problems with another one in which my answer fails to match the one in the text:

Problem: (2x[sup:1zpkh3lh]3[/sup:1zpkh3lh]+5x[sup:1zpkh3lh]2[/sup:1zpkh3lh]-22x+10)/(2x-3)

I approached the problem using polynomial long division.

The answer I obtain is: x[sup:1zpkh3lh]2[/sup:1zpkh3lh]+4x+5 with a remainder of 25, so it would look like x[sup:1zpkh3lh]2[/sup:1zpkh3lh]+4x+5+25/2x-3

The answer in the book is: x[sup:1zpkh3lh]2[/sup:1zpkh3lh]+4x-5-5/(2x-3)

I understand that the -5 multiplied by the -5 = 25, which would be equivalent to my answer.

Question: what is the relevance of the book representing its answer in such a way, rather than in the way I do?
 
kitsae said:
The answer I obtain is … x[sup:1di7rzjx]2[/sup:1di7rzjx] + 4x + 5 + 25/(2x-3)
Click to expand...


This is not correct.

-
The answer in the book is: x[sup:1di7rzjx]2[/sup:1di7rzjx] + 4x - 5 - 5/(2x - 3)

I understand that the -5 multiplied by the -5 = 25
Click to expand...


No, you do not understand (heh, heh).

-5 - 5/(2x - 3) means subtraction, not multiplication.

In other words, negative five is not being multiplied by -5.

5/(2x - 3) is being subtracted from -5.

It looks to me like you made a mistake near the last step of your division.

2x goes into -10x negative 5 times, not 5 times. This gives the following.

-10x + 10
-10x + 15
-------------
-5

In other words, the remainder is -5, not 25.

 
You are right -- dumb mistake. I got exactly what the book has now.
 
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