The most basic cubics questions might ask you to factorise a simple cubic where a factor of x can be taken out first:
Example 1 –
Example 2 –
Example 3 –
Other cubics questions might involve factorising a more general cubic and may require knowledge of the factor theorem.
Example 1 – Given that x=-2 is a root of the cubic , factorise it completely.
Example 2 – Factorise completely. By inspection, we can see that x=1 is a root of f(x) and so (x-1) is a factor. Using polynomial division, or inspection again, we have that which factorises completely to .
You may also be required to sketch the graph of a given cubic.