Using the remainder theorem, find the remainder,

Question:

Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where $p(x)=2 x^{3}+x^{2}-15 x-12, g(x)=x+2$.

 

 

Solution:

$p(x)=2 x^{3}+x^{2}-15 x-12$

$g(x)=x+2$

By remainder theorem, when p(x) is divided by (x + 2), then the remainder = p(−2).

Putting x = −2 in p(x), we get

$p(-2)=2 \times(-2)^{3}+(-2)^{2}-15 \times(-2)-12=-16+4+30-12=6$

∴ Remainder = 6

Thus, the remainder when p(x) is divided by g(x) is 6.

 

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