These are the steps I have done thus far:Quote:

A straight line of gradient $\displaystyle m$ is drawn through the point $\displaystyle A(2, -4)$ on the curve $\displaystyle y = x^2 - 4x$. Find, in terms of $\displaystyle m$, the coordinates of the point $\displaystyle B$ at which the line intercepts the curve again.

Let $\displaystyle c$ be the $\displaystyle y$ - intercept

$\displaystyle -4 = 2m + c$

$\displaystyle c = -4 - 2m$

Hence equation of the line is $\displaystyle y = mx - 4 - 2m$

Equating this into $\displaystyle y = x^2 - 4x$,

$\displaystyle mx - 4 - 2m = x^2 - 4x$

$\displaystyle x^2 - 4x - mx + 4 + 2m = 0$

$\displaystyle x^2 - x(4 + m) + 4 + 2m = 0

$

I'm not sure how I can factorise this into the answer that is $\displaystyle (2 + m, m^2 - 4)$

Any help would be greatly appreciated and thank you very much in advance! :)