Question

If the polynomial $x^4+x^2+1$ is divided by $(x-2)$, then the reminder is ?

Answer 1

We know, the Remainder Theorem states that when we divide a polynomial $f\left(x\right)$ by $x-c$, then the remainder is $f\left(c\right)$.

Here, the given polynomial is $f\left(x\right)=x^4+x^2+1$ which is divided by $(x-2)$, then we calculate $f\left(2\right)$ to find the remainder as shown below:

$f\left(2\right)=(2{)}^4+(2{)}^2+1=16+4+1=21$.

Hence, by remainder theorem, when $f\left(x\right)=x^4+x^2+1$ is divided by $(x-2)$, the remainder obtained is $21$.