Using remainder theorem, find the remainder when p(x)

Question:

Using remainder theorem, find the remainder when $p(x)=x^{3}+3 x^{2}-5 x+4$ is divided by $(x-2)$.

 

Solution:

Given : $p(x)=x^{3}+3 x^{2}-5 x+4$

Now, $p(2)=2^{3}+3\left(2^{2}\right)-5(2)+4$

$=8+12-10+4$

$=14$

 

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