How do I find the solutions to 8x^3-x+7

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.