Question 947462: P(x) = 4x^4 + 30x^3 − 40x^2 + 36x + 11, c = −5. How to solve with synthetic division and the Remainder Theorem?
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! 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.
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