we know that
If \((x-8)\) is a factor of the function \(f(x)=-2x^{3}+17x^{2}-64\)
then
\(x=8\) is a root of the function f(x)
therefore
For \(x=8\) the value of the function must be zero
Verify
Substitute the value of \(x=8\) in the function
\(f(8)=-2(8)^{3}+17(8)^{2}-64\)
\(f(8)=-2(512)+17(64)-64\)
\(f(8)=-1,024+1,088-64\)
\(f(8)=-1,088+1,088\)
\(f(8)=0\)
therefore
the answer is
Yes, \((x-8)\) is a factor of the function f(x)
