document.write( "Question 1106649: The dimensions of a present that is a rectangular prism are given by 2x+3, x-2, and x-5. Write an equation representing the volume of the box, in the form f(x)=ax^3+bx^2+cx+d. Identify and justify all inadmissible values for x. \n" ); document.write( "
Algebra.Com's Answer #721734 by ankor@dixie-net.com(22740)\"\" \"About 
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The dimensions of a present that is a rectangular prism are given by 2x+3, x-2, and x-5.
\n" ); document.write( " Write an equation representing the volume of the box, in the form f(x)= ax^3+bx^2+cx+d.
\n" ); document.write( ":
\n" ); document.write( "f(x) = (2x+3)*(x-2)*(x-5)
\n" ); document.write( "FOIL the first two factors
\n" ); document.write( "f(x) = (2x^2 - 4x + 3x - 6)*(x-5)
\n" ); document.write( "f(x) = (2x^2 - x - 6)*(x - 5)
\n" ); document.write( "Multiply by the last factor
\n" ); document.write( "f(x) = 2x^3 - 11x^2 - x + 30 cu units is the volume
\n" ); document.write( ":
\n" ); document.write( "Identify and justify all inadmissible values for x.
\n" ); document.write( "We don't want f(x) to equal 0 or negative value
\n" ); document.write( "Graphing will illustrate this
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-50%2C+50%2C+2x%5E3-11x%5E2-x%2B30++%29+\"
\n" ); document.write( "You can see that any value for x that makes y=0 or negative value is inadmissible, namely:
\n" ); document.write( " Values equal or less than 1.5 and values equal or between 2 and 5 \n" ); document.write( "
\n" );