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Q.
When $x^3+5 x^2-k x+8$ is divided by $(x-3)$ the remainder is $k$. Find the value of $k$.
Polynomials
Solution:
$f(x)=x^3+5 x^2-k x+8$
By remainder theorem, when $f(x)$ is divided by $(x-3)$ the remainder is $f(3)$
$ =(3)^3+5(3)^2-k(3)+8 $
$ =27+45-3 k+8=80-3 k$
According to the given information,
$ 80-3 k=k $
$ \Rightarrow 4 k=80 \text { or } k=20$