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August 6th, 2011, 08:28 AM  #1 
Newbie Joined: Jul 2011 Posts: 3 Thanks: 0  Synthetic Division Problem
Hi Can anyone be kind enough to explain to me what "synthetic division"? and how I can use that to solve the following: The question says,"use synthetic division to determine if (x + 1) is a factor of P(x) = x^4 + 3x^3  2x^2 12x  8.If so ,write P(x)as (x+1)times the reduced polynomial.Then find the zeros of P(x)(with multiplicity) Graph the polynomial ,clearly labeling key parts of the graph. How do I approach this question? Thanks 
August 6th, 2011, 08:37 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Synthetic Division Problem
Synthetically divide by (x + 1). If you don't have any idea how to do that, it would be better for you to do a web search. Set x + 1 = 0 to find that x = 1 So 1 is the number "in the box". The remainder will either be 0, or not 0. 
August 7th, 2011, 01:56 PM  #3  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Synthetic Division Problem Quote:
Mulitply by and subtract it from the polynomial. Thus: Simple enough, right? Just like basic division. Continuing on: Subtract times from our polynomial, yielding: If you are confused, please note the fact that the subtraction sign is being distributed onto the thing which we're subtracting. So, it's actually subtracting the positive values rather than adding them. Continuing on, multiply by and subtract it, which yields us: To finally complete what may feel like a long problem, multiply by and subtract it: &\text{} &0 \end{align}" /> This means: =x^4+3x^32x^212x8" /> i.e. =P(x)" /> Hence, is a factor of I want to continue this problem on to find a simpler factorization: =(x+1)(x(x^2+2x4) =(x+1)(x(x(x+2)4) =(x+1)(x^2(x+2)4x =(x+1)(x^2(x+2)(x+2)4) =(x+1)(x+2)(x^24) =(x+1)(x+2)(x+2)(x2) =(x+1)(x2)(x+2)^2" /> Thus, by multiplicity: You can do the graphing. I [expletive] hate graphing.  
August 7th, 2011, 02:51 PM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Synthetic Division Problem
That's nice, but it's not synthetic division!

August 7th, 2011, 03:19 PM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Synthetic Division Problem Hello, Kodwo! If you're not familiar with Synthetic Division, I recommend a search. Quote:
[color=beige]. . . [/color] [color=beige]. = . . . . . . . . . . . . . . . [/color] [color=beige]. . . [/color] [color=beige]. . . [/color]The zeros are:[color=beige] .[/color] 1, 2, and 2 (multiplicity 2). Code:  *   * * *  * * *  * oo+o 2 1*  * 2 *  * *   
August 7th, 2011, 03:26 PM  #6  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Synthetic Division Problem Quote:
o_O. Oh well, I hope I helped in some form or another. . .  
August 7th, 2011, 03:59 PM  #7 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Synthetic Division Problem
You did polynomial long division... nothing wrong with that! Synthetic (as the abacus showed) takes up a lot less space 
August 7th, 2011, 04:01 PM  #8  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Synthetic Division Problem Quote:
 

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