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.
:
f(x) = (2x+3)*(x-2)*(x-5)
FOIL the first two factors
f(x) = (2x^2 - 4x + 3x - 6)*(x-5)
f(x) = (2x^2 - x - 6)*(x - 5)
Multiply by the last factor
f(x) = 2x^3 - 11x^2 - x + 30 cu units is the volume
:
Identify and justify all inadmissible values for x.
We don't want f(x) to equal 0 or negative value
Graphing will illustrate this 
{{{ graph( 300, 200, -10, 10, -50, 50, 2x^3-11x^2-x+30  ) }}}
You can see that any value for x that makes y=0 or negative value is inadmissible, namely:
 Values equal or less than 1.5 and values equal or between 2 and 5