How do you use the remainder theorem to find the remainder of #P(x) = x^4 - 9x^3 - 5x^2 - 3x+4 div x+3#?

1 Answer
Alan P.
Oct 23, 2015

According to the Remainder Theorem the remainder of a polynomial,#P(x)#, divided by #(x+3)# is #P(-3)#
Remainder #P(-3)= 292#

Explanation:

One method of evaluating #P(-3)# is to use "synthetic substitution" as demonstrated below:

#{: (,"|",1,-9,-5,-3,4), (-3,"|",,-3,36,-93,288), (,,"-----","-----","-----","-----","-----"), (,,1,-12,31,-96,), (,,,,,,R=292) :}#

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