SOLUTION: Shipping boxes come in various sizes and shapes. Consider a box with a square base, whose base length must be greater than 5 cm. The volume in cubic centimeters, V, of this box is

Algebra ->  Rational-functions -> SOLUTION: Shipping boxes come in various sizes and shapes. Consider a box with a square base, whose base length must be greater than 5 cm. The volume in cubic centimeters, V, of this box is       Log On


   

Question 1202704: Shipping boxes come in various sizes and shapes. Consider a box with a square base, whose base length must be greater than 5 cm. The volume in cubic centimeters, V, of this box is given as V(x) = 3x^3+24x^2+15x-150. Write a combined function to represent the area of the base, A(x), if the side length of the base is x + 5.
A(x) is x^2+10x+25
b) Determine the combined function h(x)=V(x)/A(x). Hint: Express h(x) in simplified form. What does this function represent in the context of the scenario?
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The description indicates you have all you need to solve the problem's question/s.

h%28x%29=V%2FA=%283x%5E3%2B24x%5E2%2B15x-150%29%2F%28x%2B5%29%5E2



3%28x%5E3%2B8x%5E2%2B5x-50%29 for V. 

Synthetic division, twice for 'checking' root  -5,

    -------------------------
-5  |   1   8   5   -50
    |      -5  -15   50
    |__________________________
        1   3  -10   0


-5   |  1   3   -10
     |     -5    10
     |_________________________
        1  -2    0

highlight%28h%28x%29=3%28x-2%29%29

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Hint: V%28x%29+=+3x%5E3%2B24x%5E2%2B15x-150 factors to V%28x%29+=+3%28x-2%29%28x%2B5%29%5E2
You can use the rational root theorem to determine this.