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.