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

Apr 26, 2016

$6 {x}^{2} - 6 x - 11 x + 11 = \left(6 x - 11\right) \left(x - 1\right)$

#### Explanation:

Factor by grouping:

$6 {x}^{2} - 6 x - 11 x + 11$

$= \left(6 {x}^{2} - 6 x\right) - \left(11 x - 11\right)$

$= 6 x \left(x - 1\right) - 11 \left(x - 1\right)$

$= \left(6 x - 11\right) \left(x - 1\right)$

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

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

$6 {x}^{2} - 17 x + 11$

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 $\left(x - 1\right)$ is a factor.