When f(x)is divided by x-1 and x+2,the remainders are 4 and -2 respectively . Hence find the remainder when f(x)is divided by x^2+x-2 .

To find the remainder when f(x) is divided by x^2 + x - 2, we will make use of the Remainder Theorem.

According to the Remainder Theorem, if f(x) is divided by (x - a), then the remainder will be equal to f(a). So, in this case, when f(x) is divided by (x - 1), the remainder is 4, which means f(1) = 4.

Similarly, when f(x) is divided by (x + 2), the remainder is -2, which means f(-2) = -2.

Now, to find the remainder when f(x) is divided by x^2 + x - 2, we will use polynomial long division.

Dividing f(x) by x^2 + x - 2, we get:

4x + 6
____________________
x^2 + x - 2 | f(x)
- (x^2 + 3x)
_________________
-2x - 2
+ (2x + 4)
_________________
2

The remainder is 2.

Therefore, when f(x) is divided by x^2 + x - 2, the remainder is 2.