### Introduction

Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations . These have the general form:

$\phantom{\rule{2em}{0ex}}{a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\dots +{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}=0$

in which $x$ is a variable and ${a}_{n},{a}_{n-1},\dots ,{a}_{2},{a}_{1},{a}_{0}$ are given constants. Also $n$ must be a positive integer and ${a}_{n}\ne 0$ . Examples include ${x}^{3}+7{x}^{2}+3x-2=0,\phantom{\rule{1em}{0ex}}5{x}^{4}-7{x}^{2}=0$ and $-{x}^{6}+{x}^{5}-{x}^{4}=0$ . In this Section you will learn how to factorise some polynomial expressions and solve some polynomial equations.

#### Prerequisites

• be able to solve linear and quadratic equations

#### Learning Outcomes

• recognise and solve some polynomial equations