$\"\"$

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The volume of the container is $\"\"$ .

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The dimensions of container is $\"\"$ .

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$\"\"$ .

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Substiute $\"\"$ in $\"\"$ .

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$\"\"$

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Identify Possible Rational Zeros:

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Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

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The polynomial is $\"\"$ .

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Because the leading coefficient is $\"\"$ , the possible rational zeros are the intezer factors of the constant term $\"\"$ .

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$\"\"$ or

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$\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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Perform the synthetic substitution method by testing $\"\"$ and $\"\"$ .

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is a zero of $\"\"$ .

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Therefore, $\"\"$ is a rational zero.

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The depressed polynomial is $\"\"$ .

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$\"\"$

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The depressed polynomial $\"\"$ has no real zeros.

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Therefore, $\"\"$ is a rational zero.

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Therefore, $\"\"$ is the factor of $\"\"$ .

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The value of $\"\"$ is $\"\"$ .

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The dimensions of the container is

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$\"\"$

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$\"\"$

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The dimensions of the container is 1 inch, 5 inch, and 9 inch.