SOLUTION: The volume of a rectangular box is V(x)=(6x^3+29x^2-7x-10)cm^3. The box has a length of (2x+1)cm and a width of (x+5)cm. Determine the height of the box. thanks for your time :)

Algebra ->  Inequalities -> SOLUTION: The volume of a rectangular box is V(x)=(6x^3+29x^2-7x-10)cm^3. The box has a length of (2x+1)cm and a width of (x+5)cm. Determine the height of the box. thanks for your time :)      Log On


   

Question 999752: The volume of a rectangular box is V(x)=(6x^3+29x^2-7x-10)cm^3. The box has a length of (2x+1)cm and a width of (x+5)cm. Determine the height of the box.
thanks for your time :)
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a rectangular box is V(x)=(6x^3+29x^2-7x-10)cm^3. The box has a length of (2x+1)cm and a width of (x+5)cm. Determine the height of the box.
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Divide the cubic by one of the binomials, then by the other.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The volume of a rectangular box is
V%28x%29=%286x%5E3%2B29x%5E2-7x-10%29cm%5E3.
The box has a length of %282x%2B1%29cm and a width of+%28x%2B5%29cm.
Determine the height of the box.
V%28x%29=%286x%5E3%2B29x%5E2-7x-10%29cm%5E3...since V%28x%29=length%2Awidth%2Aheight+, means %282x%2B1%29cm and +%28x%2B5%29cm two of factors and the height is third factor; so,
factor given equation completely
V%28x%29=%286x%5E3%2B29x%5E2-7x-10%29cm%5E3...write 29x%5E2 as 33x%5E2-4x%5E2 and -7x as 15x-22x
V%28x%29=6x%5E3%2B33x%5E2-4x%5E2%2B15x-22x-10...group
V%28x%29=%286x%5E3-4x%5E2%29%2B%2833x%5E2-22x%29%2B%2815x-10%29
V%28x%29=2x%5E2%283x%5E3-2%29%2B10x%283x-2%29%2B5%283x-2%29
V%28x%29=%283x-2%29+%282x%5E2%2B11x%2B5%29
V%28x%29=%283x-2%29+%282x%5E2%2Bx%2B10x%2B5%29
V%28x%29=%283x-2%29+%28%282x%5E2%2B10x%29%2B%28x%2B5%29%29
V%28x%29=%283x-2%29+%282x%28x%2B5%29%2B%28x%2B5%29%29
V%28x%29=%283x-2%29+%282x%2B1%29+%28x%2B5%29

so, the height is: %28x%2B5%29cm