PSAT/NMSQT Practice Exam

Having a factor means the polynomial equals zero when x takes the value that makes the factor zero. If k − x is a factor, then evaluating at x = k should give zero: P(k) = k^2 + n k^2 = (1 + n)k^2 = 0. Since k ≠ 0, k^2 ≠ 0, so 1 + n must be 0, yielding n = -1. Only this value makes the expression vanish at x = k; other choices leave (1 + n)k^2 nonzero.