Question

when polynomial p(x) is divided by x-1 and x-2 the remainder are 5 and 7 respectively. find the remainder when p(x) is divided (x-1)(x-2)​

Answer 1

solution

Let us assume the polynomial to be f(x) .When f(x) is divided by (x−1) , we get the remainder as 5 .Therefore, f(1)=5 When f(x) is divided by (x−2) , we get the remainder as 7 .

.Therefore, f(2)=7 Now, when same polynomial f(x) is divided by (x−1)(x−2) , the remainder is given by:f(x)=q(x).(x−1)(x−2)+r(x) When, x=1⇒f(1)=0.(x−2)q(1)+r(1)=5 When, x=2 ⇒f(2)=0.(x−1)q(2)+r(2)=7 Solving above two equations, we get remainder r(x)=2x+3

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