Question

What is x cubed minus 8

Answer 1

Since
`x^3-8` is a sum of cubes, (-8 is -2 cubed) it can be factored like so:


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


`a^3=x^3\implies a=x`

`b^3=-8\implies b=-2`


`x^3-8=(x+(-2))(x^2-x(-2)+(-2)^2)=\boxed{(x-2)(x^2+2x+4)}`