請幫我用多項式解題拜託! 1. x^2+8x+15=(x-k)^2-1，則k=?

Sol
x^2+8x+15
=(x^2+8x)+15
=(x^2+2*x*4)+15
=(x^2+2*x*4+16)+15－16
=(x+4)^2－1
k=－4

x² + 8x + 15 = (x-k)² -1
x² + 8x + 15 = x² -2kx + k² -1
=> 8x = -2kx . . . . . . . . . . . . .①
=> 15 = k² -1 . . . . . . . . . . . . ②
從 ① 8 = -2k => k = -4
從 ② 15 = k² -1 => k² =16 => k = ± 4

k = -4 或 k = 4 (rejected)
∴ k = -4 (Ans)