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**Very Interesting Question on Division of Polynomials!!**

**1. Question: 'When a polynomial f(x)= x^4 - 6x^3 + 16x^2 - 25x + 10 is divided by another polynomiall g(x)= x^2 - 2x + k, the remainder is x+a. Find the value of a k and a'.**

## Homework Equations

**3. I tried solving it by using long division with f(x) as the dividend and g(x) as the divisor, and I figured out the remainder in terms of k and equated it with x+a; this was my first equation. After that, I used the realtion of dividend-remainder=quotient*divisor, taking the remainder in terms of 'a'. This was my second equation.**

After that, I subtracted my first equation from my second, so that the 'a' cancelled out, and got an equation of purely 'k', but the equation still had the variable 'x' in it, so I'm stuck again.

I need help, is my approach to the question wrong?After that, I subtracted my first equation from my second, so that the 'a' cancelled out, and got an equation of purely 'k', but the equation still had the variable 'x' in it, so I'm stuck again.

I need help, is my approach to the question wrong?