#### notes

Let us now discuss how we can factorise expressions in one variable, like `x^2 + 5x + 6, y^2 – 7y + 12, z^2 – 4z – 12, 3m^2 + 9m + 6,` etc.

Observe that these expressions are not of the type `(a + b)^2` or `(a – b)^2`, i.e., they are not perfect squares.

In general, for factorising an algebraic expression of the type

`x^2 + px + q,` we find two factors a and b of q (i.e., the constant term) such that

ab = q and a + b = p

Then, the expression becomes `x^2 + (a + b) x + ab`

or `x^2 + ax + bx + ab`

or x(x + a) + b(x + a)

or (x + a) (x + b) which are the required factors.