What is (k) to make (x^2-8x+k) a perfect square?

Correct answer: (16)

Direct answer: C, 16. A perfect square should have the form \((x-m)^2=x^2-2mx+m^2\). Compare this with \(x^2-8x+k\). We need \(-2m=-8\), so \(m=4\), and therefore \(k=m^2=16\). Indeed, \(x^2-8x+16=(x-4)^2\). Option A, 4, is only half the needed coefficient and gives \(x^2-8x+4\), not a square. Option B, 8, is the magnitude of the middle coefficient, not its half squared. Option C is correct. Option D, 64, squares 8 directly, but the rule requires squaring half of the coefficient of x. Memory cue: for \(x^2+bx+c\), the completing-square value is \(c=(b/2)^2\); the sign disappears after squaring.