Question:
Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where $p(x)=3 x^{4}-6 x^{2}-8 x-2, g(x)=x-2$.
Solution:
$p(x)=3 x^{4}-6 x^{2}-8 x-2$
$g(x)=x-2$
By remainder theorem, when p(x) is divided by (x − 2), then the remainder = p(2).
Putting x = 2 in p(x), we get
$p(2)=3 \times 2^{4}-6 \times 2^{2}-8 \times 2-2=48-24-16-2=6$
∴ Remainder = 6
Thus, the remainder when p(x) is divided by g(x) is 6.