Question

Find the remainder when $p\left(x\right)=x^4-3x^2+4x+5$, is divided by $g\left(x\right)=x^2+1-x$

Answer 1

We divide the given polynomial $p\left(x\right)=x^4-3x^2+4x+5$ by $g\left(x\right)=x^2-x+1$ as shown in the above image:

From the above division, we observe that the quotient is ${}^2+x-3$ and the remainder is $8$.

Hence, the remainder is $8$.