Showing posts with label Math Tips and Advice. Show all posts
Showing posts with label Math Tips and Advice. Show all posts

Saturday, November 30, 2013

How can you graph in a simple way?

simple way...?
Simple is a subjective word, but the most basic way is to just choose some values of one of the variable and compute values of other variables. Then plot the resulting points. The art/skill of choosing good values can be developed with practice. As with any mathematics the key to success is practice.

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