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Simplifying g(x) = x(x + 5)(x + -5)(x + 1) * 2 Multiply g * x gx = x(x + 5)(x + -5)(x + 1) * 2 Reorder the terms: gx = x(5 + x)(x + -5)(x + 1) * 2 Reorder the terms: gx = x(5 + x)(-5 + x)(x + 1) * 2 Reorder the terms: gx = x(5 + x)(-5 + x)(1 + x) * 2 Reorder the terms for easier multiplication: gx = 2x(5 + x)(-5 + x)(1 + x) Multiply (5 + x) * (-5 + x) gx = 2x(5(-5 + x) + x(-5 + x))(1 + x) gx = 2x((-5 * 5 + x * 5) + x(-5 + x))(1 + x) gx = 2x((-25 + 5x) + x(-5 + x))(1 + x) gx = 2x(-25 + 5x + (-5 * x + x * x))(1 + x) gx = 2x(-25 + 5x + (-5x + x2))(1 + x) Combine like terms: 5x + -5x = 0 gx = 2x(-25 + 0 + x2)(1 + x) gx = 2x(-25 + x2)(1 + x) Multiply (-25 + x2) * (1 + x) gx = 2x(-25(1 + x) + x2(1 + x)) gx = 2x((1 * -25 + x * -25) + x2(1 + x)) gx = 2x((-25 + -25x) + x2(1 + x)) gx = 2x(-25 + -25x + (1 * x2 + x * x2)) gx = 2x(-25 + -25x + (1x2 + x3)) gx = 2x(-25 + -25x + 1x2 + x3) gx = (-25 * 2x + -25x * 2x + 1x2 * 2x + x3 * 2x) gx = (-50x + -50x2 + 2x3 + 2x4) Solving gx = -50x + -50x2 + 2x3 + 2x4 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'x'. g = -50 + -50x + 2x2 + 2x3 Simplifying g = -50 + -50x + 2x2 + 2x3
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