Posted tagged ‘Algebra’

Oops… Was that your battleship? (updated!)

March 14, 2010

The space on which linear functions are drawn is sometimes called the X-Y Plane, because it is made up of two number lines at right angles – the horizontal numberline (X -axis) and the vertical numberline (Y-axis), and defines a flat 2- dimensional area (a plane). It is properly known as the Cartesian Plane, named by RenĂ© Descartes. You may be familiar with games that use a similar system, like Battleship. Battleship isn’t quite a Cartesian Plane, since it uses letters on the horizontal axis. A game that uses the cartesian plan better is Bug hunt – which requires you to find the shortest path (via “manhattan distance” – you don’t have to understand this, but it is interesting!)

But before we can get to playing with the algebra of lines on a cartesian plane, we need to master some simple algebra first – the algebra of expansion and factorisation. We need to be able to deal with distributive law – the rule for multiplying brackets (1, 2, 3) like this:

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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.

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