# Polynomials

A list of resources to support the teaching and learning of Polynomials in A level mathematics.

### Functions and Graphs

These resources cover aspects of functions and graphs and are suitable for students studying mathematics at A Level.

Topics covered include an introduction to functions, the hyperbolic, trigonometric and **polynomial functions**, as well as inverse functions and limits of functions.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of functions and graphs will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided

### Polynomials

This resource contains three activities exploring polynomials.

**Th e Gold and Silver Cuboid** requires students to find a connection between the volume of a cuboid, the surface area and the edge length. The second part of the activity asks students to find the maximum and minimum volume of a cuboid gives certain constraints.

**Venn Diagrams** is a task whereby students are given a Venn diagram and asked to find a quadratic function for each region of the Venn diagram.

**Remainders** requires students to test and prove a conjecture using the remainder theorem

### Numerical Methods

This activity **Polynomial Equations** **with Unit Coefficients **sets students the task of finding the roots of polynomials with a large number of terms.

Students are required to use a graph plotter to compare the graphs of several polynomials looking for common points and differences. The task leads to a numerical method, iteration, to find roots of the polynominals.

### Factorising Cubics and Quartics Powerpoints

These PowerPoint presentations demonstrate a variety of methods which can be used to factorise polynomials.

The techniques include factorising cubics and quartics by inspection; using a table and algebraic long division.

### Cyclotomic Polynomials

Cyclotomic polynomials are explained in this presentation, which uses a regular polygon to illustrate the complex roots of unity and establish which of those are primitive, before demonstrating some intriguing algebra.

The activity is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon.