Question

Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain.
A. Yes. When the function f(x) = -2x3 + 17x2 - 64 is divided by x - 8, the remainder is zero. Therefore, x - 8 is a factor of f(x) = -2x3 + 17x2 - 64.
B. No. When the function f(x) = -2x3 + 17x2 - 64 is divided by x - 8, the remainder is zero. Therefore, x - 8 is not a factor of f(x) = -2x3 + 17x2 - 64.
C. Yes. When the function f(x) = -2x3 + 17x2 - 64 is divided by x - 8, the remainder is not zero. Therefore, x - 8 is a factor of f(x) = -2x3 + 17x2 - 64.
D. No. When the function f(x) = -2x3 + 17x2 - 64 is divided

Answer 1

well the easy thing to do is use the factor theorem

if (x - 8) is a factor then x = 8 should result in f(8) being zero..

so just substitute

\[f(8) = -2(8)^3 + 17(8)^2 - 64\]

hope this helps.

Answer 2

So (x - 8) is a factor, and I just have to use Long Division of Polynomials to figure it out?

Answer 3

well yes... its a bit of a tedious process when you can use the factor theorem to prove it.

I'd ask your teacher why you can't use the factor theorem to show it.

Answer 4

You guys rock! Thanks! :D

Answer 5

glad to help