Answer:
A
![f(x) = x^3 - 2x^2 -3x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%202x%5E2%20-3x%20%2B%206)
Step-by-step explanation:
According to the Factor Theorem, if (<em>x</em> - <em>k</em>) is a factor of a polynomial P(x), then P(k) must equal zero.
We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let <em>k</em> = 2, √3, -√3.
So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.
Testing each choice, we can see that only A is true:
![\displaystyle f(x) = x^3 - 2x^2 - 3x + 6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20x%5E3%20-%202x%5E2%20-%203x%20%2B%206)
Testing all three values yields that:
![\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20f%282%29%20%26%3D%20%282%29%5E3%20-%202%282%29%5E2%20-3%282%29%20%2B%206%20%5C%5C%20%26%3D%20%288%29%20-%20%288%29%20-%286%29%20%2B%20%286%29%20%5C%5C%20%26%3D%200%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D0%20%5C%5C%20%5Cdisplaystyle%20%20f%28%5Csqrt%7B3%7D%29%20%26%3D%20%28%5Csqrt%7B3%7D%29%5E3%20-%202%28%5Csqrt%7B3%7D%29%5E2%20-%203%28%5Csqrt%7B3%7D%29%20%2B%206%20%5C%5C%20%26%3D%283%5Csqrt%7B3%7D%29%20-%286%29-%283%5Csqrt%7B3%7D%29%20%2B%206%20%5C%5C%20%26%3D%200%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D0%20%5C%5C%20f%28-%5Csqrt%7B3%7D%29%20%26%3D%20%28-%5Csqrt%7B3%7D%29%5E3%20-%202%28-%5Csqrt%7B3%7D%29%5E2%20-%203%28-%5Csqrt%7B3%7D%29%20%2B%206%20%5C%5C%20%26%3D%28-3%5Csqrt%7B3%7D%29%20-%286%29%2B%283%5Csqrt%7B3%7D%29%20%2B%206%20%5C%5C%20%26%3D%200%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D0%20%20%20%5Cend%7Baligned%7D)
Hence, our answer is A.
Answer:
80 people preferred apples, and 110 people preferred strawberries.
Step-by-step explanation:
Percentages can also be expressed as a fraction in decimal form. So 32% is equal to 0.32. In order to get the value for the percentage of a number, you multiply the decimal of the percentage by the number. So for apples: 32% of 250 is 0.32 multiplied by 250, and you get 80. For strawberries: 0.44 times 250 equals 110.
Answer:
Bedroom 1 and 2
Step-by-step explanation:
The area of Bedroom 1 is 121, which is less than 132.
The area of Bedroom 2 is 120, which is also less than 132.
The area of Bedroom 3 is 169, which is more than 132.
Answer:
58 seconds.
Step-by-step explanation:
Since one minute equals 60 seconds, Carlos took 63 seconds.
Orlando ran in 63 seconds - 5 seconds, which is equal to 58 seconds.