Question

x be a polynomial of degree more than 2
when p(x) is divided by x-2 lt leaves remainder 1
and when it is divide by, X-3, 1t leves remainder3

Find the remainder when p(x) is
divided by (x-2) (X-3)​

Answer 1

Answer:The remainder of division by a degree polynomial will be a degree 1 polynomial, that is, something in the form ax + b. Hence we have, for any polynomial p, there exists a polynomial q and numbers a and b such that:

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

By remainder theorem, the remainder from division by (x - a) of p is given by p(a). Hence, the remainder from dividing by (x - 2) is p(2) = 1, and similarly p(3) = 3

Hence:

p(2) = q(2)(2 - 3)(2 - 2) + 2a + b = 1

2a + b = 1 ... (1)

Step-by-step explanation: