Unit 1: REMAINDER THEOREM, FACTOR THEOREM, AVERAGE GRADIENT, LIMITS AND FIRST PRINCIPLE

INTRODUCTION

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

LEARNING OUTCOME

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

LESSON NOTES

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.