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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +

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Magoosh GMAT Instructor
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +  [#permalink]

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New post Updated on: 17 Oct 2012, 04:32
1
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:35) correct 21% (02:35) wrong based on 140 sessions

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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20


For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/

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Originally posted by mikemcgarry on 16 Oct 2012, 11:07.
Last edited by Bunuel on 17 Oct 2012, 04:32, edited 1 time in total.
Renamed the topic.
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Re: hard factoring problem  [#permalink]

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New post 16 Oct 2012, 11:21
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mikemcgarry wrote:
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20



6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (ax+b)(cx+d)
Hence a=2, b=c=3, d=-4

So, 2+3+3+ |-4| = 2+3+3+4 = 12

Answer B.
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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +  [#permalink]

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New post 24 Jul 2015, 04:21
mikemcgarry wrote:
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20


For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/


mikemcgarry
This should be 700+ as you describe in your blog right?
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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +  [#permalink]

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New post 24 Jul 2015, 05:04
\(6x^2 + x - 12 = 6x^2 + 9x - 8x - 12 = 3x(2x+3) - 4(2x+3) = (3x-4) (2x+3)\)

\((3x-4) (2x+3) = (ax+b) (cx+d)\)

therefore, \(a = 3, b = -4, c = 2, d = 3\).

\(|a| + |b| + |c| + |d| = |3| +|-4| +|2| +|3| = 3+4+2+3 = 12\). Ans (B).
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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +  [#permalink]

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New post 24 Jul 2015, 11:22
reto wrote:
This should be 700+ as you describe in your blog right?

Dear reto,
I'm happy to respond. :-) This is a rather challenging question, about as hard as the GMAT Quant would ever ask. It's rare that they would ask you to factor a quadratic with a lead coefficient other than 1.

Nevertheless, I am of the opinion that the idea of a "700+ question" is suspect and possibly flawed. See this blog article:
http://magoosh.com/gmat/2014/is-this-a- ... -question/

Does this make sense?
Mike :-)
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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +  [#permalink]

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New post 05 Oct 2017, 13:08
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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + &nbs [#permalink] 05 Oct 2017, 13:08
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