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.