Question:
Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where $p(x)=2 x^{3}-7 x^{2}+9 x-13, g(x)=x-3$.
Solution:
$p(x)=2 x^{3}-7 x^{2}+9 x-13$
$g(x)=x-3$
By remainder theorem, when $p(x)$ is divided by $(x-3)$, then the remainder $=p(3)$.
Putting $x=3$ in $p(x)$, we get
$p(3)=2 \times 3^{3}-7 \times 3^{2}+9 \times 3-13=54-63+27-13=5$
∴ Remainder = 5
Thus, the remainder when p(x) is divided by g(x) is 5.