[ALGEBRA 2 POLYNOMIAL DIVISION/REMAINDER THEOREM] Help!!! I'm desperate to find the answer, will give brainliest to first person that answers the question in the photo!

  k = -4

Step-by-step explanation:

The remainder theorem tells you that the remainder from division f(x)/(x -k) is f(k). You want the value of k such that ...

  f(k) = -15

Looking on the given graph, you find that k must be -4. That is, ...

  f(-4) = -15

  k = -4

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The divisor with k=-4 is (x -(-4)) = (x +4). The second attachment shows the division of f(x) by (x+4). The remainder is shown on the bottom line.