Question

please solve with full solution fast ​

Answer 1

Step-by-step explanation:

F(x) = (x-1) q(x) + 5 …..1

F(x) = (x-2) q'(x) + 7 ……2

So F(1) = 5 and F(2) = 7.

Now F(x) is divided by (x-1)(x-2) it's is a polynomial of degree two.

Reminder should be a polynomial of degree less then 2. Say.. r=ax+b

Now.. F(x) = (x-1)(x-2) q”(x) + r

F(x) = (x-1)(x-2) q”(x) + (ax+b). ………3

@x=1. 5= a+b

@x=2. 7= 2a+b

Solve two equations and get the value of a and b. That's the ans.

r = 2x+3.