Saturday, November 30, 2013

Factorize m^4+m^2+1

Factoring isn't easy, until you get good at it. One useful technique is to introduce terms that add to 0 as follows:

m%5E4%2Bm%5E2%2B1=m%5E4-m%5E3%2Bm%5E3%2Bm%5E2%2B1

m%5E4-m%5E3%2Bm%5E3%2Bm%5E2%2B1=%28m%5E4%2Bm%5E3%2Bm%5E2%29%2B%281-m%5E3%29
now we can write...

rearranging and grouping leads to
%28m%5E2%2Bm%2B1%29%28m%5E2-m%2B1%29

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