Question

How do you factor `x^3 - 16`?

Answer 1

Set this expression to `0` to determine a root; then use synthetic division to determine the second factor

If `x^3 - 16 =0`
then
`x^3 = 16`
and
`x = 2root(3)(2)`

So
`(x-2root(3)(2))`
is a factor of `x^3-16`

Use synthetic division to divide `(x-2root(3)(3))`
into `(x^3-16)`
giving
`(x^2+2root(3)(2)x + 4root(3)4)`

So
`(x^3-16)`
`=(x-2root(3)(2))(x^2+2root(3)(2)x + 4root(3)4`