Using the remainder theorem, find the remainder,
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.

 

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