document.write( "Question 623310: A open tray is to be made from a 8.5-inch by 12-inch piece of sheet metal by cutting squares of equal size from each corner and bending up the flaps, write a formula for the volume of the tray as a polynomial function...I think it starts out like this V(x)=4x(12-2x)(8.5-2x) but Im not sure. \n" ); document.write( "

Algebra.Com's Answer #392117 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Except for the 4, your formula is exactly correct. The general formula for volume of this shape (rectangular prism) is:
\n" ); document.write( "V = l*w*h
\n" ); document.write( "You got the length and width right. But the height is just x, not 4x. So the volume of your tray is:
\n" ); document.write( "V(x)=x(12-2x)(8.5-2x)

\n" ); document.write( "This is not a polynomial, however. So we need to multiply it out. Distributing the x we get:
\n" ); document.write( " $\"V%28x%29=%2812x-2x%5E2%29%288.5-2x%29\"$
\n" ); document.write( "Now we use FOIL to multiply the rest:
\n" ); document.write( " $\"V%28x%29=12x%2A8.5+%2B+12x%2A%28-2x%29+%2B+%28-2x%5E2%29%2A8.5+%2B+%28-2x%5E2%29%2A%28-2x%29\"$
\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"V%28x%29=102x+%2B+%28-24x%5E2%29+%2B+%28-17x%5E2%29+%2B+4x%5E3\"$
\n" ); document.write( " $\"V%28x%29=102x+%2B+%28-41x%5E2%29+%2B+4x%5E3\"$
\n" ); document.write( "Normally we write polynomials in order from highest exponent to lowest:
\n" ); document.write( " $\"V%28x%29=4x%5E3+%2B+%28-41x%5E2%29+%2B+102x\"$ \n" ); document.write( "

\n" );