## Quartics

A quartic is a polynomial of 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 with and two real linear factors : 7. two real quadratic factors each with  If the coefficient of is positive the graph tends to infinity as If is fully factorised into real linear factors, then

 For a distinct factor thegraph cuts the x - axis at  For each squared factor thegraph touches the x - axis at  If has a cubed factor thegraph cuts the x - axis at and has a point of inflecion at  If has a quadruple factor the graph touches the x - axis but is a minimum at that point. If a quartic with has one realquadratic factor with wehave If a quartic with has two realquadratic factors both with we have  