Polynomials

What is the coefficient of x^3 when 24x^4 + 6x^3 + 4x^2 + 7x - 5 is multiplied by 6x^3 + 3x^2 - 3x + 4 and the like terms are combined?

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$(24x^4 + 6x^3 + 4x^2 + 7x - 5) ( 6x^3 + 3x^2 - 3x + 4)$

$=144x^7+108x^6-30x^5+132x^4+3x^3-20x^2+43x-20$

$=x(x(x(x(x(x(144x+108)-30)+132)+3)-20)+43)-20$

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