An algebra problem by Vivek Parimi

Algebra Level 3

\[\large x^4 + 5x^3 + 4x^2 - 3x + 9 = (x - k)^2 (ax^2 + bx + c) \]

If the above equation is an algebraic identity with integer \(k\), find the value of \(5a - 7b +8c\).

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