If 4-jx-x^2 is divided by x-4 the remainder is -4. Find k.

I meant find j

a little synthetic division shows that

(-x^2-jx+4) / (x-4)
leaves a remainder of -4j+12
So, we need j = 3

-x^2-3x+4 = (-x+1)(x+4)

To find the value of k, we need to use the Remainder Theorem. According to the Remainder Theorem, when a polynomial f(x) is divided by another polynomial x - c, the remainder is equal to f(c).

In this case, we are given that when the polynomial 4 - jx - x^2 is divided by x - 4, the remainder is -4. So we can set up the following equation:

4 - j(4) - (4)^2 = -4

Simplifying the equation, we get:

4 - 4j - 16 = -4

Combining like terms:

-12 - 4j = -4

Now, let's isolate the variable:

-4j = -4 + 12

-4j = 8

Finally, we can solve for j by dividing both sides of the equation by -4:

j = 8 / -4

j = -2

Therefore, the value of j is -2.