Question 1061025
The quadratic factor is positive everywhere.
{{{graph(300,300,-5,5,-5,5,x^2+x+1)}}}


You could try putting it into standard form, or you can just check its discriminant to see if this is negative or not.  You should find that the discriminant,,......  {{{1^2-4*1*1=1-4=-3<0}}}, so this means the quadratic factor as a function will not have points on the x-axis....


That then leaves you with the critical x value for the linear factor, and that is at x=5.


{{{linearFactor*quadraticFactor>0}}};
Check the signs in the indicated intervals to see which interval makes the inequality true and which make it false.


<pre>
INTERVAL          ANALYZE INEQUALITY     RESULT
(-infin,5)        (-)(+)>0,  FALSE       FALSE
(5,infinity)      (+)(+)>0,  TRUE        TRUE
</pre>