So, we’ve gone through two and a bit chapters of Mathematical methods so far, and you are beginning to think that you’ve done the worst of it – it can’t get that much harder, can it? Really?

Well, welcome to cubics, quartics and higher order polynomials – they are the big brothers and sisters to the humble quadratic, and they’d like to have a *word* with you about beating up on their sibling, the poor little quadratic – something about “completing **your** square”

On a more serious note, if you are feeling alright about algebra so far, the next section isn’t any harder – just a few more ideas – nothing new or harder than we’ve done so far, just more. Just like when we started quadratics, the first thing we do with cubics and quartics is to identify the common pattern, and be able to factorise them directly from recognising that pattern.

Once we can do that, we will look at how you can start to graph these functions from their intercepts – but that means we need a way of finding all the intercepts. We already knew from our studies of the Null Factor Law (NFL) that the factors of a quadratic equation can give the intercept. The Remainder theorem (right now, that irritating chorus should be going through your head) allows us to find the factors by finding values for **a** where f(a) = 0 for a given f(x). Combining all this knowledge gives us the ability to sketch almost any graph!

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