document.write( "Question 598405: If a box and it's volume are represented by the following expression V(x)= x^3 -6x^2+12x-8, what are the expressions that represent each of its dimensions?(length, width and height) \n" ); document.write( "

Algebra.Com's Answer #378597 by KMST(5328) $\"\"$ $\"About$

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$\"%28x-2%29%5E3=x%5E3-6x%5E2%2B12x-8\"$
\n" ); document.write( "so I would say it is a cube-shaped box with sides measuring $\"x-2\"$
\n" ); document.write( "You may immediately realize that it is the cube of a binomial from the formula
\n" ); document.write( " $\"%28a%2Bb%29%5E3=4%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"$ as I did.
\n" ); document.write( "Otherwise, you would start factoring, and do a bit more work, but reach the same result.
\n" ); document.write( "To start factoring, you would look for a zero of the polynomial, knowing that the possible rational zeros are:
\n" ); document.write( "-1, 1, -2, 2, -4, 4, -8, and 8.
\n" ); document.write( "Once you found that 2 is a zero you would be able to factor out $\"%28x-2%29\"$
\n" ); document.write( "and have
\n" ); document.write( " $\"V%28x%29=%28x-2%29%28x%5E2-4x%2B4%29\"$
\n" ); document.write( "The rest of the factoring would be easy. \n" ); document.write( "

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