Posted tagged ‘Polynomials’

Divide & Conquer! (updated with factor theorem)

March 14, 2010

Divide and Conquer (Latin: Divide et Impera) is an aphorism meaning to split an enemies strength and defeat each part individually – in more modern times, the same concept is called “Defeat in Detail”. You need to apply the same tactic to your studies in Mathematical Methods – there is a great amount to learn, but each individual part is not that difficult. You need to be writing your bound reference to take advantage of these separate skills, organising them so that they are easy to find. Any student who doesn’t organise their bound reference is failing to plan (and thus, planning to fail…).

But this post is not merely about study tips – it is all about conquering the polynomial long division algorithm. When we are dealing with polynomial expressions of order higher than two (i.e. highest power term is greater than or equal to 3), such as a cubic or quartic we cannot use the general solution to the quadratic equation (in most situations). We need an alternative method to factorise these expressions – Polynomial Long Dvision is the way to deal with these tricky functions.