Factorising polynomials is a basic but satisfying exercise in algebra. Try it here, with some random machine-generated examples.

Factorising is the process of turning a polynomial such as:

Into simpler factors. In this case they would be and . If you multiply the two factors together you get the original polynomial.

Notice how the 3 in the polynomial is the **sum** of the 1 and the 2 in the pair of factors.
Also how the 2 in the polynomial is the **product** of the 1 and the 2 in the two factors.

This actually wouldn't be the case if the coefficient of the x2 term weren't 1. But it's not difficult to extend the thinking to cope with these cases.

And now it's your turn.

Factorise:

Write the two factors in the form 2x+1 or x or x-3.

Factor 1: Factor 2: