# Shift by one

Algebra Level 5

Find the sum of all complex values of the parameter $$A$$, such that that polynomial \begin{align} f_A(x)=& x^6+6x^5+5x^4-30x^3-74x^2-72x \\ & +A\left(x^4+5x^3+9x^2+8x\right) \\ \end{align}

can be expressed as $$g(h(x) )$$, where $$g(x)$$ and $$h(x)$$ are non-linear polynomials with complex coefficients.

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