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

This lesson begins by looking again at the difference between equations and identities. (You might remember that we dealt with these concepts when learning about trigonometric identities in Pure Maths 1.) Once we have established the idea of an identity — particularly with regard to polynomials — we will see how we can use the identity of polynomials to solve various problems by **equating the coefficients of identical polynomials**. It's a relatively simple procedure, and you should have no difficulty with it. This lesson is also fairly short, so you will be a bit less pressurized today. (The next two lessons are fairly long, so you might want to ensure that you have some extra time available for them.)

## Equations, identities, and the principle of equating coefficients

The first video explains the difference between identities and equations, and shows what is meant by equating the coefficients of polynomials.

For your notebook:

## Equating coefficients of polynomials

If two polynomials are identically equal to each other (i.e. they are equal to each other for all values of \( x \)), then their coefficients for corresponding powers of \( x \) can be equated. Mathematically, we write this as follows:

If

\( ax^n + bx^{n-1} + ... + k \equiv Ax^n + Bx^{n-1} + ... + K \),

then

\( a = A, b = B, ..., k + K \).

## Applications of the procedure of equating coefficients

The next video shows you how to find one factor of a polynomial using the procedure of equating coefficients. (This is Example 1.3.1 from your text book.)

The next example is a little more detailed, but completely straightforward nevertheless. (This is example 1.3.2 from your text book.)

Read section 1.3 in your text book to revise the concepts explained in the videos.

You should now be able to handle the exercises quite easily.

## Weight lifting

Complete the following exercises from your text book:

Exercise 1B

- 1 a, c, e
- 2 a, c, e
- 3 a, c, e
- 4 a, c

If you are registered for this course, you can download the answer key from your download area on the My Account menu.