Verified Answer :

AndyBryer

To do this we can use the remainder theorem to find the value of the remainder when x=8
f(8)=-28³+178²-64
f(8)=0
Therefore x-8 is a factor.

\(If\ (x-8)\ is\ a\ factor\ of\ the\ function\ f(x)=-2x^3+17x^2-64\\\\then\ f(8)=0.\\\\Check:\\\\f(8)=-2\cdot8^3+17\cdot8^2-64=-2\cdot512+17\cdot64-64\\\\=-1024+1088-64=0-correct\\\\Answer:(x-8)\ is\ a\ factor\ of\ the\ function\ f(x).\)

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