Question

P(x) is a polynomial of degree more than 2 leaves remainder 1 when divided by

Answer 1

your question is incomplete ,
Complete question is ----> 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 remainder 3. Find the remainder when p(x) is divided by (x-2) (x-3) ?

solution :- Let when p(x) is divided by (x -2)(x -3) it leaves remainder (ax + b).
In Euclid algorithm, P(x) = (x-2)(x-3)g(x) + (ax + b)

we know, one thing if f(x) is divded by (x -a) then , it leaves remainder f(a).
similarly , p(x) is divided by (x -2) then, it leaves remainder p(2) , but remainder is given 1 then, p(2) = 1
p(2) = (2-2)(x -3)g(2) + (2a + b) = 1
2a + b = 1 -----------(1)

similarly , P(3) = (3-2)(3-3)g(3) + (3a+b) = 3
3a + b = 3 -------(2)

solve equations (1) and (2)
a = 2 and b = -3

hence, (ax + b) = (2x -3)

Now, come to the point , P(x) is divided (x -2)(x -3) then, it leaves the remainder (ax + b) e.g., (2x -3)

Hence, answer is $\bold{\boxed{\boxed{\text{the remainder is 2x-3}}}}$

Answer 2

THE ABOVE ANSWER IS ABSOLUTELY CORRECT!!✌️