Question:
Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where $p(x)=x^{3}-2 x^{2}-8 x-1, g(x)=x+1 .$
Solution:
$p(x)=x^{3}-2 x^{2}-8 x-1$
$g(x)=x+1$
By remainder theorem, when p(x) is divided by (x + 1), then the remainder = p(−1).
Putting x = −1 in p(x), we get
$p(-1)=(-1)^{3}-2 \times(-1)^{2}-8 \times(-1)-1=-1-2+8-1=4$
∴ Remainder = 4
Thus, the remainder when p(x) is divided by g(x) is 4.