Answer
64
Step-by-step explanation
The remainder theorem states:
when a polynomial p(x) is divided by the binomial x - a, the remainder obtained is p(a).
In this case, the polynomial is:
[tex]p(x)=(x-4)^6[/tex]
and the binomial is:
[tex]x-6[/tex]
Therefore, the remainder is obtained by evaluating p(x) at x = 6, as follows:
[tex]\begin{gathered} p(6)=(6-4)^6 \\ p(6)=2^6 \\ p(6)=64 \end{gathered}[/tex]
