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November 2nd, 2011, 06:27 AM  #1 
Newbie Joined: Nov 2011 Posts: 21 Thanks: 0  stuck simplifying a quadratic, please help
I'm practicing for the SAT, and found this questions in a Princeton Review practice test: 2x^2 + x  28 x^2  3x  28 = ? here are the options: A. 2x7 x7 B. 2x+1 x3 C. x2 x+14 D. 2 3 E. The expression cannot be simplified.  I thought the answer is E, but according to the answer key it isn't. I know that I can simplify the denominator from: x^23x28 to: (x7)(x+4) but I have no idea about the numerator. Thanks for any help. 
November 2nd, 2011, 06:36 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: stuck simplifying a quadratic, please help
a = 2 b = 1 c = 28 ac = 56 = 8*(7) So we can rewrite 2x^2 + 8x 7x 28 and factor by grouping. 
November 2nd, 2011, 06:58 AM  #3  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: stuck simplifying a quadratic, please help Quote:
1) To have we must have a=2 and b= 4 to get and . Does that work? . No, that doesn't work. 2) To have we must have a= 2 and b= 7. Does that work? . Yes!! Quote:
 
November 2nd, 2011, 12:52 PM  #4 
Newbie Joined: Nov 2011 Posts: 21 Thanks: 0  Re: stuck simplifying a quadratic, please help
I'm sorry, I've lost you. I'm probably lacking some knowledge that you assume in your explanations. To establish a starting point I can work with, here's what I do know: I know that an equation of this form [ x^2+bx+c ] can be simplified, if I can think of two numbers that sum up to [b] and multiply to [c]. If those numbers are [p] and [q], I can simplify: (x+p)(x+q). What throws me off if the coefficient of the xsquared in the equation above: [2x^2 +...] instead of [x^2 +...]. I don't know how to deal with that. If you could walk me through this again, from here, I'd appreciate it. 

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