Question 947462
Maybe you want to check if the root or binomial  (x+c) is one of the factors of P(x).  If remainder from synthetic division is 0 then Factor Theorem tells you that x+c is one of the factors of P.  If the remainder from synthetic division is not zero, then the Remainder theorem tells you that P(c)=theRemainder, or in your example, P(-5)=theRemainder.



_______________|__________
_______________|________________________________________________
_______________|________4_____30______-40_______36_______11
________-5_____|
_______________|_____________-20______-50______450______-2430
_______________|____________________________________________________
________________________4_____10______-90_______486______-2419


-5 is NOT a root of P.
P(-5)=-2419.