# How To Factorise Quadratic Expressions

Learn the basics of factorisation.

In this post, we will show you how to factorise quadratics when $$a=1$$ or $$a=-1$$. Quadratics have the standard form:

$${ax^2+bx+c}$$

The procedure is as follows:

1. Write your expression in standard form. Note the $$a$$, $$b$$ and $$c$$ values.

2. Make brackets such that $$(\,x+f_1 )\,(\,x+f_2 )\,$$, where $$f_1$$ and $$f_2$$ are factors of $$c$$ (ignore the sign).

The right factors are those that sum up to $$b$$ (sign included).

3. Look at the sign of $$c$$.

1. If $$c$$ is positive, both factors take the sign of $$b$$.
2. If $$c$$ is negative, the bigger factor takes the sign of $$b$$

Factorise the following:

1. $$y=x^2-3x-54$$

Factors of 54: $$1 \times 54$$, $$2\times 27$$, $$3 \times 18$$, $$6 \times 9$$. $$c$$ is negative, so the bigger factor should take the sign of $$b$$. The possible combination is: $${6 \times 9}$$ where $$6-9=-3$$. Therefore:

\begin{alignat} {1} y &= x^2-3x-54 \\ &= (\, x-9)\,(\,x+6 )\, \end{alignat}
2. $$y=x^2-5x+6$$

Using the procedure in (1.)

\begin{alignat} {1} y &= x^2-5x+6 \\ &= (\, x-3)\,(\,x-2 )\, \end{alignat}
3. $$y=-x^2-8x-15$$

\begin{alignat} {1} y &= -x^2-8x-15 \\ &= -(\,x^2+8x+15 )\,\\ &= -(\, x+5)\,(\,x+3 )\, \end{alignat}