Factoring is taking polynomial multiplication and reversing it. Let’s see how this works in practice.
Here the greatest common factor would be 8x to the power of three. since 8 and 64 are both divisible by 8 and the least x here is to the power of 3. In practice now you take out the 8x to the power of three and multiply it by what is left over to achieve the same result, as per below:
Take a look now at a trinomial (a polynomial with 3 terms).
This factors out to:
When multiplying this together you end up with something similar to the original trinomial.
Where mnx = (m+n)x and (m+n)=n.