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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. 2x-7 x-7 B. 2x+1 x-3 C. x-2 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^2-3x-28 to: (x-7)(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
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Quote:
 Originally Posted by Dan154 I'm practicing for the SAT, and found this questions in a Princeton Review practice test: 2x^2 + x - 28 x^2 - 3x - 28 = ?
28= 4(7) and 7- 4= 3 so the denominator factors as (x- 7)(x+ 4). In order to be able to reduce, the numerator must also have a factor of x- 7 or x+ 4.
1) To have $(x- 7)(ax+ b)= 2x^2+ x- 28$ we must have a=2 and b= 4 to get $2x^2$ and $-28$. Does that work? $(x- 7)(2x+ 4)= 2x^2- 14x+ 4x- 28= 2x^2- 10x- 28$. No, that doesn't work.

2) To have $(x+ 4)(ax+ b)= 2x^2+ x- 28$ we must have a= 2 and b= -7. Does that work? $(x+4)(2x- 7)= 2x^2+ 8x- 7x- 28= 2x^2+x- 28$. Yes!!

$\frac{2x^2+ x- 28}{x^2- 3x- 28}= \frac{(x+ 4)(2x- 7)}{(x+ 4)(x- 7)}$

Quote:
 here are the options: A. 2x-7 x-7 B. 2x+1 x-3 C. x-2 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^2-3x-28 to: (x-7)(x+4) but I have no idea about the numerator. Thanks for any help.

 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 x-squared 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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