Question

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

Answer 1

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

Here, the given polynomial is $f\left(x\right)=x^3+x^2-7x-3$ which is divided by $(x-3)$, so we calculate $f\left(3\right)$ to find the remainder as shown below:

$f\left(3\right)=(3{)}^3+(3{)}^2-(7\times 3)-3=27+9-21-3=36-24=12$

Hence, by remainder theorem, when $f\left(x\right)=x^3+x^2-7x-3$ is divided by $(x-3)$, the remainder is $12$.