SOLUTION: you are given a cube. the length, width, and height = x. if the length is increased by 12, the width is increased by 6, and the height is decreased by 4 than the volume doubles. fi

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....eq 1
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...eq 2
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take value of A from eq 1 and plug it into eq 2
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if we take the factors of plus or minus 288/1 we have possible rational roots
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if you plug 6 in you will find that to be a factor so lets use synthetic division to factor 6 out of our equation
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l 1 -14 0 288
l
6 l____ 6___-48___-288____________________________
1 -8 -48 0
so we have (x-6)(x^2-8x-48)
which can be further factored to (x-6)(x-12)(x+4)
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so x is 6,12,0r -4..since 4 is negative we throw it out
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