Could somebody tell me why are we taking p(-1) why p(+1) or something else

Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x - a) is a factor of polynomial ƒ(x).
Here, in the given question, 
If (x + 1) is a factor of given polynomial 
x + 1 = 0
x = - 1
It means p(- 1) must be 0, when we put x = -1 in the given polynomial. 
And if the value of given polynomial is not equal to 0, then the x + 1 is not a factor of given polynomial. 

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In this question x =-1 was taken because it satisfies the given polynomial means the answer comes out to be Zero, whereas if you put x=1 then the answer doesn't comes out to be equal to zero.
Therefore ,the value of x which satisfies the polynomial is the zero of the polynomial and then after puting that value equal to zero you will get the factors as well .

Hope you found it helpful
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