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 factorthegraph cuts the x - axis at For each squared factorthegraph touches the x - axis at Ifhas a cubed factorthegraph cuts the x - axis atand has a point of inflecion at Ifhas a quadruple factorthe graph touches the x - axis but is a minimum at that point. If a quartic withhas one realquadratic factor withwehave If a quartic withhas two realquadratic factors both withwe have