1. Factors

Expressing a given expression/polynomial as a product of two or more expressions/polynomials is called factorising the expression.

We will consider the factorising process of polynomials first.We saw earlier that the algebraic methods and patterns that apply to polynomials can be applied to other expressions as well, since these patterns form the basis of our work in algebra.

1.1. Common factor

When a factor is contained in every term of an algebraic expression, it is referred to as a common factor of that expression.

1.1.Factorising trinomials

1.1.1. Trinomial with leading coefficient 1

1.1.1. Trinomial with leading coefficient not 1

We will now develop methods for factorising expressions in which the leading coefficient is not one.

For the previous factors, we only considered the factors of the constant term (c) and the sum of these factors had to give us the middle term (b). This was because a = 1. Now if , then we have to adopt a different approach. (Remember, try to make a = 1 by searching for a common factor first, and only if this does not happen, we adopt the following method).

To factorise , we will have to consider the factors of both “a” and “c”. Such factors will then become rational factors, which will be discussed fully when we solve equations later on in our work. We will limit ourselves to factorising only for now.

In general