Question

The remainder when polynomial P(x) of degree 5 is divided by x+1 and x-1 is 1 and 2 respectively.Find the remainder when P(x) is divided by
$x {2} - 1$
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Answer 1

x2−1→(x+1)(x−1)

x2−1[P(x)][Q(x)]→R=ax+b

⇒(x+1)(x−1)⋅xQ(x)+ax+b=P(x)

whenx=−1→1=−a+b

whenx=1→2=a+b

solving the above equations we get, a=21,b=23

Remainder  =ax+b⇒21x+23=21(x+3)