When a polynomial #P(x)# is divided by #(x^2-1)#, the remainder is #2x+3#. What is the remainder when #P(x)# is divided by #(x-1)#?

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Answer 1 · 2017-06-04T11:20:14

#5#

According to the #P(x)# properties, we have

#P(x) = Q(x)(x^2-1)+2x+3# where #Q(x)# is the quotient polynomial.

Considering now

#P(x)=(Q(x)(x+1))(x-1)+r(x)= (Q(x)(x+1))(x-1)+a#

we can determine the value of #a# making #x=1# so

#P(1)=(Q(1)(2)) xx 0 + a = 2 xx 1+3=5#

then #r(x)=a=5#