The expression x^2− 2x + k is divisible by (x +1). Find the remainder when it is divided by (x + 3). A. 1 B. 4 C. 12 D. 16 E. 18
Using the remainder theorem if f(x) is a polynomial and (x-a) is a factor of f(x) the f(a)=0.
Since f(x) is divisible by (x+1);
When f(x) is divided by `(x+3)` the remainder is given by `f(-3)` .
`f(-3)=9+6-3 = 12`
So the remainder when f(x) is divided by (x+3) is 12.
Correct answer is C.