Further Maths - Cubics

Here, using $z$ instead of $x$ means that the variable is complex. $w$ is also sometimes used.

The first step is to find the one real solution. Since it’s a cubic, there will be three solutions and by examining the graph you can see that there always must be at least one real solution (cubics always cross the $y$-axis at least once).

For $z=1$:

For $z=-1$:

So we have one bracket, $(z+1)$. We can now write out the cubic like so:

We can work out $A,B\text{and},C$ by inspection:

• $A$ must be $1$ since the final result of multiplying everything out has a