In this unit, participants will look at the fundamental tools required for calculus, the intuitive
description of the limit and factorisation of third-degree polynomials as an enabling tool in
sketching cubic functions
At the end of this Unit, participants should be able to:
• Factorise a third-degree polynomial using the factor theorem
• Determine the average gradient between two points using functional notation
• Understand the concept of the limit and solve simple problems involving limits
• Use the concept of average gradient and limit to derive a formula for first principles
• Differentiate elementary functions using first principles
Defining polynomials
A polynomial is an algebraic expression consisting of one or more terms. All the coefficients of a
the polynomial must be constants that are real numbers, and the exponents must be integers greater
than or equal to zero.
The highest exponent of a polynomial determines its degree.