Question

Find the remainder when $x^4+4x^3-5x^2-6x+7$ is divided by $x-2$.

Answer 1

We divide $x^4+4x^3-5x^2-6x+7$ by $(x-2)$ as shown in the above image:

From the division, we observe that the quotient is $x^3+6x^2+7x+8$ and the remainder is $23$.

Hence, the remainder is $23$.