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
$x {2} - 1$
​

Answer 1

Answer:

x

2

−1→(x+1)(x−1)

x

2

−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=

2

1

,b=

2

3

Remainder =ax+b⇒

2

1

x+

2

3

=

2

1

(x+3)

Step-by-step explanation:

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