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Question

A polynomial P(x) contains only terms of even degree, when P(x) is divided by (x+1), the remainder is 2. If P(x) is divided by (x21) then find the remainder.

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Solution

f(x) is even function.
p(x)=p(x)
x21=(x+1)(x1)
Put x=1;
p(1)=p(1)=2 (Remainder)
p(x)=Q(x)(x21)+ax+b Remainder
p(1)=Q(1)(121)+a(1)+b2=a+b
p(1)=Q(1)((1)21)+a(1)+b2=a+b
____________
4=2b
b=2
a=0
Remainder=ax+b=2.

1208375_1264153_ans_c104c181997b4879ad27e9e7e3ac916c.JPG

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