Question

find quadratic expressions which has remainder of -6 when divided by x-1 , a remainder of-4 when divided by x-3 and no remainder when divided by x+1

Answer 1

Answer:

2x+3

Step-by-step explanation:

We know that the remainder from (x-1) is 5

=> P(1) = 5

We know that the remainder from (x-2) is 7

=> P(2) = 7

We need to ánd out the remainder of polynomial P(x) when divided by (x-1)(x-2) Let us say D = (x-1)(x-2), the quotient is Q and the remainder is R

The remainder will be of the format Ax + B, because it is the remainder after division by a quadratic.

P(x) = Q*D + Ax + B

P(1) = Q*0 + A + B

=> 5 = A + B 

P(2) = Q*0 + 2A + B

=> 7 = 2A + B

Solving these equations, we get A =2 and B = 3 

=> R = Ax + B

=> R =2x + 3