# Lesson 1.1 Introduction to polynomials

This is a free lesson. We trust you enjoy it!

## Introduction

Welcome to Pure Maths 2! I trust you are going to enjoy this course and that you will find it helpful now and in years to come as you study further in mathematics and use your mathematical knowledge to solve problems in a variety of fields.

Our first topic is polynomials. Whether or not you have used the term before, you have actually been working with polynomials for some years already — familiar expressions like $$2x+5$$ and $$3x^2 + 2x-7$$ are examples of polynomials. In this chapter we are going to build on what you already know, ultimately developing some useful theorems and methods for working efficiently with polynomials. If you later go on to study mathematics, physics, or engineering at university you will find that polynomials can be very helpful in solving complicated equations, so it is valuable to understand them well.

This lesson is largely revision, so you can enjoy a gentle introduction to P2!

## Definition of a polynomial

Watch the following two videos. The first introduces polynomials and the second develops a mathematical definition of polynomials.

## Non-zero polynomial

A non-zero polynomial of order $$n$$ is an expression of the form

$$ax^n + bx^{n-1} + ... + jx + k$$

where $$n$$ is an integer and $$n \ge 0$$, and

$$a,b,c ... k$$ are real numbers with $$a \ne0$$.

## Addition, subtraction and multiplication of polynomials

You are actually quite familiar already with the addition, subtraction and multiplication of polynomials. The following video gives you a brief recap.

## Simple problems involving polynomials

The next two videos work through two examples of simple problems involving polynomials. Some of the exercises follow these patterns.

## Weight lifting

Complete the following exercises from your text book:

Exercise 1A

• 1 a, b, c, d, e, f
• 2 a, b, c, d, e
• 3 a, b, c, d, e
• 4 a, b, c, d
• 5 a, c, e, g, i, k
• 6 a, c, e, g, i
• 7 a, c, e, g