SOLUTION: Problem The length, width, and height of a box are x, 2x, and 3x-5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3) Here it what I have. V= x^

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Problem The length, width, and height of a box are x, 2x, and 3x-5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3) Here it what I have. V= x^      Log On


   

Question 81129: Problem
The length, width, and height of a box are x, 2x, and 3x-5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3)
Here it what I have.
V= x^2 (x + 2)(3x - 5)
= x^2 + 6x - 10
If you put 3 in place of x the volume = 180
I don't know if I am corret and would appreciate your input and help. Thank you
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the box is length*width*height, so you did develop the correct expression for V(x). But you made a mistake simplifying the expression.
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V%28x%29=%28x%5E2%29%28x%2B2%29%283x-5%29
At this point, just plug in 3 for x to find the volume:
V%283%29=%289%29%285%29%284%29
highlight%28V%283%29=180%29inches^3
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Note: if you need to find a simplified expression for V(x) prior to finding V(3), just multiply the expression for V(x):
V%28x%29=%28x%5E2%29%28x%2B2%29%283x-5%29
V%28x%29=x%5E2%283x%5E2%2Bx-10%29
highlight%28V%28x%29=3x%5E4%2Bx%5E3-10x%29
Plug in 3 for x to be sure you get the same answer as above.
Good Luck,
tutor_paul@yahoo.com