CBSE Class 10 Answered

Dear Student,

p(x) when divided by (x-2), leaves 1 as remainder

=> p(x)/(x-2) = q₁(x) + 1/(x-2)

where q₁(x) is qotient polynomial of degree more than 1.

Similarly, p(x) when divided by (x-3), leaves 3 as remainder

=> p(x)/(x-3) = q₂(x) + 3/(x-3)

where q₂(x) is qotient polynomial of degree more than 1.

Now, when p(x) is divided by (x-2)(x-3) then,

(where q₃(x) is the polynomial obtained by difference of q₂(x) and q₁(x))

Hence the remainder left by p(x) when divided by (x-3)(x-2) is (2x-3).

Regards Topperlearning.