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:

$a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_2{x}^2+a_{1}x+a_0=0$

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 $x^3+7x^2+3x-2=0,5x^4-7x^2=0$ 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