# How do you factorise x^2 − 7 x + 12?

Mar 25, 2017

(x-3)(x-4)

#### Explanation:

It is done by splitting the middle terms such the coefficients ad up to -12 and their product is +12.

In the present case -7x can be split as -3x and -4x. The multiplication of coefficients also gives +12. Accordingly,

${x}^{2} - 7 x + 12 \to$ ${x}^{2} - 3 x - 4 x + 12$

Now pair up te terms #(x^2-3x) +(-4x +12)

Extract common factors x(x-3)-4(x-3) $\to$ (x-3)(x-4)