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If $p(x) = x^4 - 3x + 2$, then find the coefficient of the $x^3$ term in the polynomial $(p(x))^3$.
Any multiple of the x^4 term will result in a power of x greater than x^3, so you can reduce this to (-3x + 2)^3
The only term that will produce an x^3 is the (-3x) term, so the coefficient of the x^3 term is just (-3)^3 or -27.