A quartic is a polynomialof degree 4. The polynomial may factorise with between one and four factors, some of which may be repeated. The different cases are

1. four distinct linear real factors :

2. a squared real linear factor and two different real linear factors :

3. two squared real linear factors:

4. a cubed factor and one real linear factor :

5. a real linear factor raised to the fourth power:

6. one real quadratic factor withand two real linear factors :

7. two real quadratic factors each with

If the coefficient ofis positive the graph tends to infinity as

Ifis fully factorised into real linear factors, then

For a distinct factorthe

graph cuts the x - axis at

For each squared factorthe

graph touches the x - axis at

Ifhas a cubed factorthe

graph cuts the x - axis atand has a point of inflecion at

Ifhas a quadruple factor

the graph touches the x - axis but is a minimum at that point.

If a quartic withhas one real

quadratic factor withwe


If a quartic withhas two real

quadratic factors both with

we have

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