384 in³
the volume (V) of a cuboid = length × width × height
V = 12 × 4 × 8 = 384 in³ ← fourth on list
To solve this question, we use the factor theorem, and using it, the polynomial function is:
![f(x) = x^3 - 2x^2 - 3x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%202x%5E2%20-%203x%20%2B%206)
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The factor theorem means that if k is a root of f(x), f(k) = 0.
Thus, applying the factor theorem for this question, we have to choose the function for which: ![f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0](https://tex.z-dn.net/?f=f%282%29%20%3D%200%2C%20f%28%5Csqrt%7B3%7D%29%20%3D%200%2C%20f%28-%5Csqrt%7B3%7D%29%20%3D%200)
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Function 1:
![f(x) = x^3 - 2x^2 - 3x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%202x%5E2%20-%203x%20%2B%206)
Testing the values:
![f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0](https://tex.z-dn.net/?f=f%282%29%20%3D%202%5E3%20-%202%282%29%5E2%20-%203%282%29%20%2B%206%20%3D%208%20-%208%20-%206%20%2B%206%20%3D%200)
![f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0](https://tex.z-dn.net/?f=f%28%5Csqrt%7B3%7D%29%20%3D%20%5Csqrt%7B3%5E3%7D%20-%202%28%5Csqrt%7B3%7D%29%5E2%20-%203%5Csqrt%7B3%7D%20%2B%206%20%3D%20%5Csqrt%7B3%5E2%5Ctimes3%7D%20-%206%20-%203%5Csqrt%7B3%7D%20%2B%206%20%3D%203%5Csqrt%7B3%7D%20-%203%5Csqrt%7B3%7D%20%3D%200)
![f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0](https://tex.z-dn.net/?f=f%28-%5Csqrt%7B3%7D%29%20%3D%20-%5Csqrt%7B3%5E3%7D%20-%202%28-%5Csqrt%7B3%7D%29%5E2%20-%203%28-%5Csqrt%7B3%7D%29%20%2B%206%20%3D%20-%5Csqrt%7B3%5E2%5Ctimes3%7D%20-%206%20%2B%203%5Csqrt%7B3%7D%20%2B%206%20%3D%20-3%5Csqrt%7B3%7D%20%2B%203%5Csqrt%7B3%7D%20%3D%200)
Thus, since all three conditions are satisfied,
is the polynomial function.
A similar question is given at brainly.com/question/11378552
10 quarts is the greatest about becuase it is equal to 40 cups.
Answer:
0.35865 and 0.35867
Step-by-step explanation:
for this number, the hundreths thousandths place is
0.358659 (bolded)
so, since the 9 rounds up, the estimated number would be 0.35866
the numbers before would be 0.35865 and after, 0.35867