One of the root  $x^3-x^2-49x+49$ is 

$x^3-x^2-49x+49$

If sum of co-efficient of expression is $1-1-49+49=0$, then  $(x-1)$ is one of the factor

$x^2-49=0\Rightarrow x^2-7^2=0\Rightarrow (x+7)(x-7)=0$

$x=7,-7$

Factor are  $(x-1),(x-7),(x+7)$