Question

How do you factor `128x^3 - 1024`?

Answer 1

`128(x-2)(x^2+2x+4)`

Explanation:

The 2 terms have a `color(blue)"common factor"` of 128, which can be taken out.

`rArr128(x^3-8)to(A)`

`x^3-8` is a `color(blue)"difference of cubes"` which, in general, is factorised as shown.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(2/2)|)))`

using a = x and b = 2, then

`rArrx^3-8=(x-2)(x^2+2x+2^2)=(x-2)(x^2+2x+4)`

Returning to (A) the complete factorisation is.

`128x^3-1024=128(x-2)(x^2+2x+4)`