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

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(52847)   (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 = , and you have an equation

= 4000,     or

= 1000.

The solution is x = 10 inches.

Answer. The height of the tank is 10 inches.

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