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Simplifying g(x) = (x + 3)(x + -2)(x + -5) Multiply g * x gx = (x + 3)(x + -2)(x + -5) Reorder the terms: gx = (3 + x)(x + -2)(x + -5) Reorder the terms: gx = (3 + x)(-2 + x)(x + -5) Reorder the terms: gx = (3 + x)(-2 + x)(-5 + x) Multiply (3 + x) * (-2 + x) gx = (3(-2 + x) + x(-2 + x))(-5 + x) gx = ((-2 * 3 + x * 3) + x(-2 + x))(-5 + x) gx = ((-6 + 3x) + x(-2 + x))(-5 + x) gx = (-6 + 3x + (-2 * x + x * x))(-5 + x) gx = (-6 + 3x + (-2x + x2))(-5 + x) Combine like terms: 3x + -2x = 1x gx = (-6 + 1x + x2)(-5 + x) Multiply (-6 + 1x + x2) * (-5 + x) gx = (-6(-5 + x) + 1x * (-5 + x) + x2(-5 + x)) gx = ((-5 * -6 + x * -6) + 1x * (-5 + x) + x2(-5 + x)) gx = ((30 + -6x) + 1x * (-5 + x) + x2(-5 + x)) gx = (30 + -6x + (-5 * 1x + x * 1x) + x2(-5 + x)) gx = (30 + -6x + (-5x + 1x2) + x2(-5 + x)) gx = (30 + -6x + -5x + 1x2 + (-5 * x2 + x * x2)) gx = (30 + -6x + -5x + 1x2 + (-5x2 + x3)) Combine like terms: -6x + -5x = -11x gx = (30 + -11x + 1x2 + -5x2 + x3) Combine like terms: 1x2 + -5x2 = -4x2 gx = (30 + -11x + -4x2 + x3) Solving gx = 30 + -11x + -4x2 + x3 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'x'. g = 30x-1 + -11 + -4x + x2 Simplifying g = 30x-1 + -11 + -4x + x2 Reorder the terms: g = -11 + 30x-1 + -4x + x2
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