if (x-1) is a factor of the polynomial f(x)= 4x^3-4x^2-x-k, where k is a constant, find the value of k.

Answer 1

If (x-1) is a factor of the polynomial f(x), then we can use synthetic division to check if the remainder is zero.

Using synthetic division:

1 | 4 -4 -1 -k
- 4 0 -1
---------------
4 0 -1 -k-1

Since the remainder is (-k-1), in order for (x-1) to be a factor of f(x), the remainder must be zero. Therefore, we have:

-k - 1 = 0
k = -1

So the value of k is -1.