If (x − 2) is a factor of x^2 + kx − 8, what is k?

解說

The factor theorem requires f(2) = 0: 4 + 2k − 8 = 0, so 2k = 4 and k = 2. Substituting x = −2 instead gives the trap k = −2. Ignoring the square and solving 2 + k − 8 = 0 gives k = 6.