Why we have to take value 1 of x

Dear student,
The question is here solved by hit and trial method

Questions involving degree more than 2 have to be solved using hit and trial method concerning the grade you are studying.
Usually integers should be put and checked.
Start by 0 and then +1 and -1 
then +2 and -2 and so on.
Her when you will start hit and trial you will see that x=0 wont satisfy but x=1 will.
Hence x=1 is the solution.
You may try the following questions for practice
x300-3x+2
x=0 wont satisfy
x=1 will satisfy.
Hence x=1 is the solution.
Similarly x3+x2+x+1
x=0,1 wont satisfy 
But x=-1 will
Hence x=-1 is the solution
Hope that helps
Cheers!!
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