For which value will the degree of ((d+4)x^7+(d-2)x^4+15) be (4)?

Correct answer: (d=-4)

The direct answer is option B, \(d=-4\). The degree is determined by the highest power of \(x\) whose coefficient is not zero. To make the degree 4, the \(x^7\) term must disappear, so \(d+4=0\), giving \(d=-4\). Now check the next term: \(d-2=-4-2=-6\), which is not zero, so the \(x^4\) term remains. The polynomial therefore becomes \(-6x^4+15\), of degree 4. Option A, \(d=2\), removes the \(x^4\) term but leaves \(6x^7\), so its degree is 7. Option B removes only the higher-degree term and keeps the fourth-degree term. Option C gives a non-zero \(x^7\) coefficient, so the degree is 7. Option D also leaves the seventh-degree term. Exam cue: first cancel the unwanted highest power, then verify that the required lower power remains.