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
The OA is D.
I thought the correct answer was E. How can I determine the largest possible value? Experts, I would be thankful if you help me here.
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What is the largest possible value of. . .
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EconomistGMATTutor
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Hello Vincen.
We have to rewrite the expression to know the possible largest value.
$$(x+2)(3-x)(x-3)(2x+4)(2+x)^2\ =\ -2\left(x+2\right)\left(x-3\right)\left(x-3\right)\left(x+2\right)\left(x+2\right)^2$$ That implies that the original expression is equal to $$-2\left(x-3\right)^2\left(x+2\right)^4\ =\ negative\left(positive\right)\left(positive\right)\le0,\ \ \ \forall x\in\mathbb{R}.$$ So, the possible largest value is 0, and it is obtained when x=-2 or x=3.
This is why the correct answer is D.
I hope this explanation may help you.
I'm available if you'd like a follow-up.
Regards.
We have to rewrite the expression to know the possible largest value.
$$(x+2)(3-x)(x-3)(2x+4)(2+x)^2\ =\ -2\left(x+2\right)\left(x-3\right)\left(x-3\right)\left(x+2\right)\left(x+2\right)^2$$ That implies that the original expression is equal to $$-2\left(x-3\right)^2\left(x+2\right)^4\ =\ negative\left(positive\right)\left(positive\right)\le0,\ \ \ \forall x\in\mathbb{R}.$$ So, the possible largest value is 0, and it is obtained when x=-2 or x=3.
This is why the correct answer is D.
I hope this explanation may help you.
I'm available if you'd like a follow-up.
Regards.
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