Question

How do you factor the trinomial `3x^2-6x-9`?

Answer 1

`=3(x-3)(x+1)`

Explanation:

`3x^2-6x-9`

`=3(x^2-2x-3)`

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

`=3(x(x-3)+1(x-3))`

`=3(x-3)(x+1)`

Answer 2

`3(x-3)(x+1)`

Explanation:

The first step is to take out the `color(blue)"common factor"` of 3

`rArr3x^2-6x-9=3(x^2-2x-3)`

Now we require to factorise the quadratic inside the bracket.

Need 2 factors which multiply to give - 3 and sum to - 2

These are -3 and +1

`rArrx^2-2x-3=(x-3)(x+1)`

`rArr3x^2-6x-9=3(x-3)(x+1)`