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

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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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);

`f(-1)=0`

`f(-1)=1+2+K=0`

`k=-3`

`f(x) =x^2-2x-3`

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.

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