Question

How do you factor `6x^2 - 6x - 11x + 11`?

Answer 1

`6x^2-6x-11x+11=(6x-11)(x-1)`

Explanation:

Factor by grouping:

`6x^2-6x-11x+11`

`=(6x^2-6x)-(11x-11)`

`=6x(x-1)-11(x-1)`

`=(6x-11)(x-1)`

Note that the hard/fun part has been done for you already in the question - the splitting of the middle term into `-6x-11x`.

Commonly this would not be done for you: The problem would be given in the form:

`6x^2-17x+11`

and it would be up to you to find the split.

In this particular case there is a shortcut: Notice that the sum of the coefficients is `0`. That is: `6-17+11 = 0`. When the sum of the coefficients is `0`, then `x=1` is a zero and `(x-1)` is a factor.