Question

When a polynomial p(x) is divided by (x - 1), the remainder is 3. When p(x) is divided by (x - 3), the
remainder is 5. If r(x) is the remainder when p(x) is divided by (x - 1) (X - 3), then the value of r(-2) is :​

Answer 1

Answer:

r(2)=0

Step-by-step explanation:

When p(x) is divided by (x - 1), the remainder is 3.

so p(1)=3

and When p(x) is divided by (x - 3), the remainder is 5.

so p(3)=5

Let r(x)= ax+b

So p(x) =(x-1)(x-3)k + r(x)

p(x) =(x-1)(x-3)k + ax +b

So on putting x=1

P(1)=a+b=3----------------------(1)

and p(3)=3a+b=5------------(2)

on subtracting (1) from(2)we get

2a=2,a=1

And from(1)

1+b=3,b=2

THus r(x)=ax+b=x+2

And r(-2)=-2+2=0