Question

How do you factor the expression `x^2-x-42`?

Answer 1

`(x+6)(x-7)`

Explanation:

`x^2-x-42`

`=> x^2-7x+6x-42`

`=> x(x-7)+6(x-7)`

`=> (x+6)(x-7)`

Answer 2

`(x+6)(x-7)`

Explanation:

The coefficient of `x^2` is `bb1`, so the factors will be of this form:

`(x +a)(x+b)`

We are looking for an `bba` and a `bb(b)` such that:

`axxb=-42`

`a+b=-1`

Possible factors for `a xx b =-42` are:

`-1 xx 42`

`1 xx 42`

`2xx-21`

`-2xx21`

`6xx-7`

`-6xx7`

`3xx-14`

`-3xx14`

The sum has to equal -1.

We can see that the only factors with a sum of `-1` is `6 and -7`.

`6+(-7)=-1`

These are the required values:

`(x+6)(x-7)`

Expanding:

`(x+6)(x-7)=x^2-x-42`

As required.

With practice you will quickly find the required values without having to list them all.