Using the remainder theorem, find the remainder,
Question:

Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where $p(x)=2 x^{3}-7 x^{2}+9 x-13, g(x)=x-3$.

 

Solution:

$p(x)=2 x^{3}-7 x^{2}+9 x-13$

$g(x)=x-3$

By remainder theorem, when $p(x)$ is divided by $(x-3)$, then the remainder $=p(3)$.

Putting $x=3$ in $p(x)$, we get

$p(3)=2 \times 3^{3}-7 \times 3^{2}+9 \times 3-13=54-63+27-13=5$

∴ Remainder = 5

Thus, the remainder when p(x) is divided by g(x) is 5.

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