Question

What could be an example of finding algebraic factor of a number ?

Answer 1

Factoring is also a particularly important step in the solution of many algebraic problems.

For example, the polynomial equation x^2 − x − 2 = 0 can be factored as (x − 2)(x + 1) = 0. Since in and integral domain a·b = 0 implies that either a = 0 or b = 0, the simpler equations x − 2 = 0 and x + 1 = 0 can be solved to yield the two solutions x= 2 and x = −1 of the original equation.

Another Example: w⁴ − 16

w⁴ − 16 = (w²)² − 4²

Yes, it is the difference of squares

w⁴ − 16 = (w² + 4)(w² − 4)

And "(w² − 4)" is another difference of squares

w⁴ − 16 =
(w² + 4)(w + 2)(w − 2)

That is as far as I can go (unless I use imaginary numbers)
i hope this is the example that you are looking for.