Answer:
x-8 is a factor of f(x)
Step-by-step explanation:
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
We are given the function
[tex]f(x)=-2x^3+17x^2-64[/tex]
And it's required to find if x-8 is a factor of f.
Applying the mentioned theorem, we only have to find f(8):
[tex]f(8)=-2\cdot 8^3+17\cdot 8^2-64[/tex]
Operating:
[tex]f(8)=-2\cdot 512+17\cdot 64-64[/tex]
[tex]f(8)=-1024+1088-64[/tex]
[tex]f(8)=0[/tex]
Thus, x-8 is a factor of f(x)
