A polynomial f(x) leaves remainder 1 and 2 when divided by x-1 and x-2 respectively. What is the remainder when f(x) is divided by (x-1) (x-2)?
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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.
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.
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