Question

What are the imaginary solutions of the polynomial equation x^3-8=0? Please Show Work

Answer 1

First factor as a difference of cubes. Can you do that?

Answer 2

Yeah. It's 2.

Answer 3

That doesn't answer my question. You found the real root, sure, which means \(x-2\) is a factor. What's the other factor?

Answer 4

x+2?

Answer 5

If you don't know the difference of cube formula, use long or synthetic division to find the other factor(s)

Answer 6

I don't know how to find the other root.

Answer 7

I don't understand.

Answer 8

Difference of cubes:\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 9

(x-8)(x^2+8x+64) ???