Cubic in Factor Form

What is Cubic in Factor Form?

A cubic written as a product of three linear factors displays its three x-intercepts directly, one from each factor set equal to zero. Multiplying the constant terms of the factors gives the y-intercept, and the sign of the leading coefficient fixes the end behaviour: a positive leading coefficient means the curve falls to the left and rises to the right. Between consecutive roots the sign of the product is constant, so the four sign intervals determine which sections of the curve lie above the x-axis and which lie below it.

This definition is part of the Equations, Inequalities and Graphs chapter in Cambridge O Level Additional Mathematics.

Concepts related to Cubic in Factor Form

• sign intervals
• end behaviour
• cusp