# Cubics

The most basic cubics questions might ask you to factorise a simple cubic where a factor of x can be taken out first.

**Example**: . Note that the discriminant of is which is negative and so has no roots. It follows that the original cubic cannot be factorised further.

Other cubics questions might involve factorising a more general cubic and may require knowledge of the factor theorem. See Example 2.

# Sketching Cubics

- Identify whether the cubic is positive or negative
- Substitute x=0 to identify the y-intercept.
- Factorise and set y=0 to identify the roots. Note that, in for example, x=-1 is a repeated root and the curve must touch the x-axis at x=-1.
- Place the graph on the axes so that all the above criteria are satisfied.

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### Example 2

- Given that is a root of the cubic , factorise it completely.
- Factorise completely.