How do you use the remainder theorem to find the remainder for each division #(x^5+32)div(x+2)#?

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Answer 1 · 2016-12-17T11:05:13

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the Remainder theorem states :

if a polynomial #" "P(x)" "#is divided by #" "(x-a)" "# the remainder is #" "P(a)" "#

proof:

#P(x)=(x-a)Q(x)+R#

#P(a)=cancel((a-a)Q(x))+R#

#:.P(a)=R#

#(x^5+32)-:(x+2)#

#P(x)=(x^5+32)#

to find remainder

#P(-2)=(-2)^5+32=-32+32=0#

remainder #" "=0" "#which implies #" "(x+2)" "#is a factor of#" " (x^5+32)#