math factorization

2011-11-21 7:11 am
I am not a great observer. So I want to ask how are we able to find the factorization of the numerator? Are there any equation that can help us?


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更新1:

To wy: I understand the way of doing that. But like in the first sight, when you see 1- z^-3, how do you know using the factor (1-z^-1) and (1+z^-1 + z^-2) Like in 1 - x^3 , how do you know it is (1 - x)( 1 + x + x^2) when you first see it?

回答 (1)

2011-11-21 3:55 pm
✔ 最佳答案
Put z^-1 = x, so the numerator becomes 1 - x^3 = (1 - x)( 1 + x + x^2).
= ( 1 - z^-1)[1 + z^-1 + z^(-2)]


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