Question

How do you factorise x^2 − 7 x + 12?

Answer 1

(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 -7x+12->` `x^2-3x-4x +12`

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

Extract common factors x(x-3)-4(x-3) `->` (x-3)(x-4)