Factorisation — Formula Sheet

When a polynomial is expressed as the product of two or more expressions, each expression is a factor of the polynomial.

Factorisation = reverse of multiplication

x^2 - y^2 = (x + y)(x - y)

When each term has a common factor, divide each term by this factor and keep the common factor outside the bracket.

6a^2 - 3ax = 3a(2a - x)

An expression with an even number of terms can be resolved into factors if arranged in groups with common factors.

ab + bc + ax + cx = (a + c)(b + x)

Split b into two parts such that their sum is b and their product is ac.

If b^2 - 4ac is a perfect square, the trinomial ax^2 + bx + c is factorisable.

x^2 + 5x + 6 = (x + 3)(x + 2)

For example, 6a^2-3ax = 3a(2a-x).