Question

Let p(x) be 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)......... Find the answer fast with proper xplanation

Answer 1

Answer:

2 x - 3

Step-by-step explanation:

Given Let p(x) be 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...

Given  p(x) be a polynomial of degree more than 2. Then the remainder p(x) is divided by (x -2) and (x - 3)

p(x) = (x - 2)(x - 3) z(x) + (ax + b)-----------(1)

Remainder is p(a) when p(x) / x - a

Remainder is 1 when p(x) / x - 2

So p(2) = 1

1 = (2 -2)(2 - 3) z(2) + (2a + b)-----------from (1)

So 2a + b = 1 ----------(2)

When p(x) / x - 3 leaves remainder 3

p(3) = 3

So from (1) we have

3 = (3 - 2)(3 -3)z(3) + 3a + b

3a + b = 3---------(3)

from 2 and 3 we get

2a + b = 1

3a + b = 3

subtracting we get

a = 2 and b = - 3

Remainder is 2 x - 3