How do you factor the expression x^2 - x - 6?

1 Answer
Dec 3, 2015

x^2 - x - 6 = (x - 3)(x + 2)

Explanation:

There are many possible ways to gain the factorisation. Let me show you one of them.

You would like to have something like

x ^2 - x - 6 = (x + a)(x + b)
color(white)(xxxxxxxii) = x^2 + (a+b)x + a*b

So, your goal is to determine a and b so that

{ (a + b = -1), ( color(white)(x) a * b = -6) :}

hold.

This approach is not always possible or can be complicated if your solutions are not integers.
Here, however, it's one of the easiest ways to compute the result. :-)

You know that a * b = -6 can be achieved either with -3 * 2 = -6 or with 3 * (-2) = -6.

Let's test which pair works for the first equation:
-3 + 2 = -1 works perfectly well, so it's a = -3 and b = 2.

Thus, your factorization is:

x^2 - x - 6 = (x - 3)(x + 2).