SOLUTION: 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. Iden

Algebra ->  Equations -> SOLUTION: 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. Iden      Log On


   

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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%28+300%2C+200%2C+-10%2C+10%2C+-50%2C+50%2C+2x%5E3-11x%5E2-x%2B30++%29+
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