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November 2nd, 2011, 06:27 AM   #1
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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.
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November 2nd, 2011, 06:36 AM   #2
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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.
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November 2nd, 2011, 06:58 AM   #3
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Re: stuck simplifying a quadratic, please help

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 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:
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.
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November 2nd, 2011, 12:52 PM   #4
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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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