Question

Algebraically find the exact real zeros and state the multiplicity of each.
f(x) = 32x^3 - 4

Answer 1

well I'd divide by 32 so x^3 - 1/8 1/8 = (1/2)^3 so you are factoring x^3 - (1/2)^3

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Answer 2

let a x and b = 1/2 and substitute

Answer 3

so the real zero is x = 1/2 from 1st bracket and 2 brackets (x^2 + 1/2x + 1/4) have unreal roots...

Answer 4

Click on the link to see the two Complex solutions.

http://www.wolframalpha.com/input/?i=0%3D+4x%5E2%2B2x%2B1