Question

Ques 7. A polynomial of degree grewter than three leaves remainder 2,6,12 when divided

Answer 1

Remainder from (x-2) is 1

remainder from (x-3) is 3

now we have to find remainder after divided by (x-2)(x-3)

let quotient be Q, and remainder is 'R' of the format is ax+b

p(x)=Q*D+ax+b

p(1)=Q*0+2a+b

1=2a+b

p(2)=Q*0=3a+b

3=3a+b

on solving we get a=2, b=-3

p(x)=(x-2)(x-3)q(x)+(2x-3)

Hence remainder is 2x-3

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