Question

The remainder obtained when the polynomial $x^4-3x^3+9x^2-27x+81$ is divided by $(x-3)$ is:

• A. $0$
• B. $3$
• C. $81$
• D. $27$

Answer 1

The correct option is C $81$

The remainder theorem states that when $f\left(x\right)$ is divided by $x-a$ then the remainder is given by $f\left(a\right)$.

So, the given function $f\left(x\right)$:

$f\left(x\right)=x^4-3x^3+a{x}^2-27x+81$
when divided by $(x-3)$, according to the remainder theorem will give remainder $f\left(3\right)$:
$f\left(3\right)=3^4-3^4+3^4-3^4+81$$=81$
$\therefore$, remainder is $81$.