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# If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?

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Math Revolution GMAT Instructor
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31 Jul 2016, 08:58
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:22) correct 17% (01:25) wrong based on 58 sessions

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If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?
A. 0
B. 25
C. -25
D. 24
E. -24

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Re: If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?  [#permalink]

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31 Jul 2016, 09:29
1
Given, (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f)

using formula a^2 - b^2 = (a+b)(a-b), we can get

(x^3-2x^2+x-1)^2-1 = (x^3-2x^2+x-1+1)(x^3-2x^2+x-1-1)

= (x^3-2x^2+x)(x^3-2x^2+x-2)
= x(x^2-2x+1)(x^3-2x^2+x-1-1)

No need to solve further, we can see one of the factors of x would be equal to see when the above equation is equated to zero.

Hence, abcdef = 0.
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Re: If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?  [#permalink]

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03 Aug 2016, 09:30
as there is no value of x apart from it being raised to cube or square & the only integer being 1
looking at the options also one can say
abcdef = 0
Math Revolution GMAT Instructor
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Re: If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?  [#permalink]

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04 Aug 2016, 19:17
If we substitute x=0, from (-1)^2-1=(-a)(-b)(-c)(-d)(-e)(-f)=abcdef, we get abcdef=0.
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Re: If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?  [#permalink]

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26 Sep 2017, 01:36
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Re: If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=? &nbs [#permalink] 26 Sep 2017, 01:36
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