If k - x is a factor of the expression x - 29nk², what must be true about k?

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Multiple Choice

If k - x is a factor of the expression x - 29nk², what must be true about k?

Explanation:
Using the Factor Theorem, if k − x is a factor of the polynomial in x, then plugging in x = k must give zero. So evaluate P(k) = k − 29 n k^2 and set it to zero: k − 29 n k^2 = 0. Factor out k to get k(1 − 29 n k) = 0, which gives two possibilities: k = 0 or k = 1/(29 n). Typically k is treated as a positive parameter in this kind of problem, and n is taken as a positive integer. In that common setup, k cannot be zero, and 1/(29 n) is positive, so k must be greater than zero.

Using the Factor Theorem, if k − x is a factor of the polynomial in x, then plugging in x = k must give zero. So evaluate P(k) = k − 29 n k^2 and set it to zero: k − 29 n k^2 = 0. Factor out k to get k(1 − 29 n k) = 0, which gives two possibilities: k = 0 or k = 1/(29 n).

Typically k is treated as a positive parameter in this kind of problem, and n is taken as a positive integer. In that common setup, k cannot be zero, and 1/(29 n) is positive, so k must be greater than zero.

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