Question #60e34

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Answer 1 · 2016-10-01T17:38:38

#r(x) = -2x+5#

Calling

#P(x) = (x-3)^200 - (x-2)^100# and
#p(x) =x^2 -5x+6 = (x-2)(x-3) #

we have

#P(x) = p(x)Q(x)+r(x)# in which

#Q(x)# is the quocient polynomial and
#r(x) = a x + b# is the remainder

Then we have

#P(2) = 1 = 2 a + b# and
#P(3) = -1 = 3 a + b#

Solving for #a,b# we have #a = -2, b= 5# so

#r(x) = -2x+5#