Divisibility condition by undetermined coefficients

Find the condition that $x^{3} - 3 p x + 2 q$ may be divisible by a factor of the form $x^{2} + 2 a x + a^{2}$ .

~12 minAnswer checked instantlypolynomial divisibilityundetermined coefficientsroots of polynomials

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 6

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).