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If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) =

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If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) = [#permalink]

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New post 17 Sep 2012, 15:23
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Last edited by Bunuel on 17 Sep 2012, 15:37, edited 1 time in total.
Edited the question.
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Re: If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) = [#permalink]

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New post 17 Sep 2012, 15:45
carcass wrote:
If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) =

(A) 3x + 7
(B) 3x – 7
(C) 3x + 1
(D) x + 7
(E) x – 7


APPROACH #1:

\(6x^2 + 11x - 7=(2x-1)(3x+7)\), therefore \(\frac{6x^2 + 11x - 7}{2x -1}=\frac{(2x-1)(3x+7)}{2x-1}=3x+7\).

Answer: A.

Solving and Factoring Quadratics:
http://www.purplemath.com/modules/solvquad.htm
http://www.purplemath.com/modules/factquad.htm


APPROACH #2:

For \(x=1\) we'll have \(\frac{6x^2 + 11x - 7}{2x -1}=\frac{10}{1}=10\). Now, plug \(x=1\) into the answer choices to see which one yields 10. Only answer choice A works.

Answer: A.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer (for example in this case for x=0 both C and D give the same result). In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
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Re: If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) = [#permalink]

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New post 17 Sep 2012, 16:45
Thanks Mod :)

All is clear and thanks for links.

one question: for me generally is not difficult to factor out an expression, for instance : x^2 – 5x – 6 = (x – 6)(x + 1). the sum or difference must give -5 and times must give -6.

Ok, in our scenario we do not have a pair of factors for 7 and 11 because primes. At most we could use quadratic formula to figure out if I have positive solution zero or negative (2 solutions, one or no solution, accordingly), but this formula doesn't resolve our problem as in the first solution. Infact purple math says ""unfactorable over the integers"

So, in the end when we encounter something like 6x^2 + 11x - 7 what we have to think first ?? Can you have a suggest ??

Thanks Bunuel
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Re: If x ≠ − 1/2, then (6x^2 + 11x - 7) / (2x -1) =   [#permalink] 17 Sep 2012, 16:45
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