Question

What is the remainder when (x - 4)6 is divided by x - 6?16-16064

Answer 1

64

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:

`p(x)=(x-4)^6`

and the binomial is:

`x-6`

Therefore, the remainder is obtained by evaluating p(x) at x = 6, as follows:

`\begin{gathered} p(6)=(6-4)^6 \\ p(6)=2^6 \\ p(6)=64 \end{gathered}`