Find the value of $k$ if $5{{x}^{5}}+2k{{x}^{3}}-6k{{x}^{2}}+9$ has a remainder of $22$ when d

Question

Find the value of $k$ if $5{{x}^{5}}+2k{{x}^{3}}-6k{{x}^{2}}+9$ has a remainder of $22$ when divided by $x-1$.

Accepted Answer

$k=-2$

Finding an Unknown using Remainder Theorem