Question

Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain?

Answer 1

Well, can you factor out x-8 from the function? If that's not working out for you, try dividing it out. Basically, that means you get the large f(x) part and write it out like this:

So the first term we put up top there multiplies with (x-8) to get rid of the largest power term in f(x). Then you multiply it out, and subtract it off, and keep going. I'll help you along, try it.

Answer 2

When x=8,
\[\space \space \space \space f(8)=-2(-8)^3+17(-8)^2-64\]

When you solve this you will get. \[f(8)=0\]
Therefore according to factor theorem (x-8) is a factor of f(x).

Hope you know about the factor theorem. :)