Find all zeros by factoring each function.

Question

Find all zeros by factoring each function. F(x)=x3+8 

Answer 1

f(x)=x^3+8 is the sum of two cubes

x^3+2^3=0

the general rule for factoring the sum of two cubes is a^3+b^3=(a+b)(a^2-ab+b^2)

using the rule...

(x+2)(x^2-2x+4)=0

x+2=0

x=-2 is one root

x^2-2x+4

use the quadratic formula

[2±√4-16]/2

[2±√-12]/2

[2±2√3√-1]/2

[2±2i√3]/2   (i=√-1)

1±i√3 are the other two roots (1+i√3 and 1-i√3)

now you have the three zeroes or roots