Answer:
[tex](x-8)[/tex] is not a factor of the function [tex]f(x) = x^{3}-9\cdot x^{2}+12\cdot x - 17[/tex].
Step-by-step explanation:
If [tex](x-8)[/tex] is a factor of the function [tex]f(x) = x^{3}-9\cdot x^{2}+12\cdot x - 17[/tex] if and only if [tex]f(8) = 0[/tex]. We must evaluate the polynomial at given value of [tex]x[/tex] to confirm or discard the statement:
[tex]f(8) = 8^{3}-9\cdot (8)^{2}+12\cdot (8) -17[/tex]
[tex]f(8) = 15[/tex]
Which means that [tex](x-8)[/tex] is not a factor of the function [tex]f(x) = x^{3}-9\cdot x^{2}+12\cdot x - 17[/tex].
