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.
