Question

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

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 $f\left(x\right)=x^3-3x^2+4x+5$ which is divided by $(x-2)$, then we calculate $f\left(2\right)$ to find the remainder as shown below:

Then,

$f\left(2\right)=(2{)}^3-3(2{)}^2+4\left(2\right)+5$

$=8-3\left(4\right)+8+5$

$=8-12+8+5$

$=21-12=9$.

Hence, by remainder theorem, when $f\left(x\right)=x^3-3x^2+4x+5$ is divided by $(x-2)$, the remainder obtained is $9$.