Question

Is x-8 a factor of the function f(x)=-2x^3+17x^2-64?

Answer 1

`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).`

Answer 2

To do this we can use the remainder theorem to find the value of the remainder when x=8
f(8)=-2*8³+17*8²-64
f(8)=0
Therefore x-8 is a factor.