Question

8. p (x) is a polynomial of degree more than 2 . When p (x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3 it leaves a remainder 3. Find the remainder when p (x) is divided by (x-2)(x-3).

Answer 1

Hello,

here is your answer :))


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We know , p(x)=g(x)q(x)+r(x)

so,

p(x)=(x−2)q1(x)+1

and

p(x)=(x−3)q2(x)+3

put x=2 in first equation and x=3 in second equation.

p(2)=1   and   p(3)=3

when p(x) is divided by (x−2)(x−3)

let remainder,r(x)=ax+b

then,

p(x)=(x−2)(x−3)q(x)+ax+b

put x=2 and x=3, we get

p(2)=2a+b   ...(1)

and

p(3)=3a+b   ...(2)

subtract (2) from (1), we get

p(2)−p(3)=2a−3a

1−3=−a

−2=−a

so, a=2

and from (1)

1=2(2)+b

so, b=−3

therefore r(x)=2x−3   ANS...

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Hope it helps u !!!!

ALL THE BEST AHEAD :))

# Nikky