SOLUTION: (x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inch

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inch      Log On


   



Question 1001645: (x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE
A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inches of water. what is the height of the fish tank?

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
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(x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE?
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TRUE.

It is TRUE because  x=3  is the root of the polynomial  f(x):   f(3) = 0.   (Check it !).

Use the  remainder theorem  (see the lesson  Divisibility of polynomial f(x) by binomial x-a  in this site).

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A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inches
of water. What is the height of the fish tank?
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Let  x  be the height of the fish tank.
Then its length is  L = 2x  and its width is  W = 2x inches too,  according to the condition.
(I assume that the tank is full,  although you didn't mention it).

Hence,  the water volume is  V = L*W*H = (2x)*(2x)*x = 4x%5E3,  and you have an equation

4x%5E3 = 4000,     or

x%5E3 = 1000.

The solution is  x = 10 inches.

Answer.  The height of the tank is  10 inches.