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Simplifying g(x) = 9x3(17x + 5)(12x2 + 1x + 16) Multiply g * x gx = 9x3(17x + 5)(12x2 + 1x + 16) Reorder the terms: gx = 9x3(5 + 17x)(12x2 + 1x + 16) Reorder the terms: gx = 9x3(5 + 17x)(16 + 1x + 12x2) Multiply (5 + 17x) * (16 + 1x + 12x2) gx = 9x3(5(16 + 1x + 12x2) + 17x * (16 + 1x + 12x2)) gx = 9x3((16 * 5 + 1x * 5 + 12x2 * 5) + 17x * (16 + 1x + 12x2)) gx = 9x3((80 + 5x + 60x2) + 17x * (16 + 1x + 12x2)) gx = 9x3(80 + 5x + 60x2 + (16 * 17x + 1x * 17x + 12x2 * 17x)) gx = 9x3(80 + 5x + 60x2 + (272x + 17x2 + 204x3)) Reorder the terms: gx = 9x3(80 + 5x + 272x + 60x2 + 17x2 + 204x3) Combine like terms: 5x + 272x = 277x gx = 9x3(80 + 277x + 60x2 + 17x2 + 204x3) Combine like terms: 60x2 + 17x2 = 77x2 gx = 9x3(80 + 277x + 77x2 + 204x3) gx = (80 * 9x3 + 277x * 9x3 + 77x2 * 9x3 + 204x3 * 9x3) gx = (720x3 + 2493x4 + 693x5 + 1836x6) Solving gx = 720x3 + 2493x4 + 693x5 + 1836x6 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'x'. g = 720x2 + 2493x3 + 693x4 + 1836x5 Simplifying g = 720x2 + 2493x3 + 693x4 + 1836x5
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