Answer:
x = -1
Step-by-step explanation:
You can use rational root test to check for rational roots.
Factors of 8: 1, 2, 4, 8
Factors of 7: 1, 7
Possible rational roots: ±1/1, ±1/2, ±1/4, ±1/8, ±7/1, ±7/2, ±7/4, ±7/8
Checking, we find that -1 is a root. Knowing that, we can use grouping to factor:
8x³ − x + 7
8x³ + 8x² − 8x² − x + 7
8x² (x + 1) − (8x² + x − 7)
8x² (x + 1) − (8x − 7) (x + 1)
(8x² − (8x − 7)) (x + 1)
(8x² − 8x + 7) (x + 1)
Using the quadratic formula, we find that 8x² − 8x + 7 has no real solutions.
Therefore, the only solution is x = -1.
![\frac{V_1}{V_2}=k^3 \\ \\ \frac{320 \ cm^3}{1080 \ cm^3}=k^3 \\ \frac{8}{27}=k^3 \\ k=\sqrt[3]{\frac{8}{27}} \\ \boxed{k=\frac{2}{3}} \Leftarrow \hbox{answer B}](https://tex.z-dn.net/?f=%5Cfrac%7BV_1%7D%7BV_2%7D%3Dk%5E3%20%5C%5C%20%5C%5C%0A%5Cfrac%7B320%20%5C%20cm%5E3%7D%7B1080%20%5C%20cm%5E3%7D%3Dk%5E3%20%5C%5C%0A%5Cfrac%7B8%7D%7B27%7D%3Dk%5E3%20%5C%5C%0Ak%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B8%7D%7B27%7D%7D%20%5C%5C%0A%5Cboxed%7Bk%3D%5Cfrac%7B2%7D%7B3%7D%7D%20%5CLeftarrow%20%5Chbox%7Banswer%20B%7D)
