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# What is the largest possible value of the following expression

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What is the largest possible value of the following expression [#permalink]

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16 Oct 2014, 23:21
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What is the largest possible value of the following expression $$(x+2)(3-x)(x-3)(2x+4)(2+x)^2$$

A. -846
B. 54
C. 12
D. 0
E. can’t be determined
[Reveal] Spoiler: OA

Last edited by Gnpth on 16 Oct 2014, 23:51, edited 2 times in total.

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What is the largest possible value of the following expression [#permalink]

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17 Oct 2014, 00:01
(3-x) is negative if x>3
(x-3) is negative if x<3

The balance terms will always be positive as they reduce to 2(x+2) to the power of 4 which is always positive.

So for all x values except for x=3 the total expression yields a negative number.
If x=3 it is multiplication with one term being zero, so the answer is zero

Zero is the largest possible value - so D.

Last edited by JohanH on 17 Oct 2014, 04:06, edited 2 times in total.

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What is the largest possible value of the following expression [#permalink]

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17 Oct 2014, 01:07
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Raihanuddin wrote:
What is the largest possible value of the following expression $$(x+2)(3-x)(x-3)(2x+4)(2+x)^2$$

A. -846
B. 54
C. 12
D. 0
E. can’t be determined

Factor -1 from the second multiple (3-x) and 2 from the 4th multiple (2x+4):

$$(x+2)(3-x)(x-3)(2x+4)(2+x)^2=-2(x+2)(x-3)(x-3)(x+2)(2+x)^2=$$
$$=-2(2+x)^4*(x-3)^2=-(some \ nonnegative \ value)$$. So, the max value of the expression is 0.

Answer: D.
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Re: What is the largest possible value of the following expression [#permalink]

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02 Nov 2015, 07:44
if x is positive, then the whole expression will result in a negative number, since we have 4 positive numbers and 1 negative number. If x is 0, again same thing. To maximize the expression, we need to make sure that at least one of the expressions results in 0. this can be done only if x is =-2 or x=3. So the maximum possible result is 0.

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Re: What is the largest possible value of the following expression [#permalink]

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09 Nov 2015, 21:26
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as (3-x)(x-3) is here to make It largest, max value of x=3 . For x=3 largest value of the expression = 0
ans:D
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Re: What is the largest possible value of the following expression [#permalink]

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24 Aug 2017, 13:34
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Re: What is the largest possible value of the following expression   [#permalink] 24 Aug 2017, 13:34
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# What is the largest possible value of the following expression

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