Answer:
(x - 4) is not a factor because [tex]f(4) \neq 0[/tex].
Step-by-step explanation:
According to the factor theorem, if f(x) = 0, only then f(x) can have a factor (x-a) which in this case is equal to (x - 4).
Considering this factor theorem, we can write it as:
[tex]f(x) = x^{5} - 3x^{4} - x - 3[/tex]
Now to check if (x - 4) is its factor or not, substitute a value of 4 in place of x in f(x):
[tex]f(4) = (4)^{5} - 3(4)^{4} - (4) - 3[/tex] [tex] = 249[/tex]
So f(x) is not equal to zero which means (x - 4) is not a factor of [tex]x^{5} - 3x^{4} - x - 3[/tex]
