For which value will the degree of ((d-8)x^8+(d+2)x^5+17) be (5)?

Correct answer: (d=8)

Direct answer: Option B, \\(d=8\\). To make the degree 5, the x^8 term must vanish and the x^5 term must remain. The x^8 coefficient is d-8, so d-8=0 gives d=8. At this value, the x^5 coefficient is d+2=10, which is nonzero. The polynomial becomes \\(10x^5+17\\), so its degree is 5. Option A, d=-2, removes the x^5 term but leaves coefficient -10 on x^8, giving degree 8. Option B satisfies both required conditions. Option C, d=0, leaves a nonzero x^8 coefficient -8, so degree 8. Option D, d=5, leaves coefficient -3 on x^8, again giving degree 8. The important check is two-part: cancel every power higher than the requested degree, then verify the requested power survives.