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Simplifying g(x) = (x2 + 4x + -12)(x + -3) Multiply g * x gx = (x2 + 4x + -12)(x + -3) Reorder the terms: gx = (-12 + 4x + x2)(x + -3) Reorder the terms: gx = (-12 + 4x + x2)(-3 + x) Multiply (-12 + 4x + x2) * (-3 + x) gx = (-12(-3 + x) + 4x * (-3 + x) + x2(-3 + x)) gx = ((-3 * -12 + x * -12) + 4x * (-3 + x) + x2(-3 + x)) gx = ((36 + -12x) + 4x * (-3 + x) + x2(-3 + x)) gx = (36 + -12x + (-3 * 4x + x * 4x) + x2(-3 + x)) gx = (36 + -12x + (-12x + 4x2) + x2(-3 + x)) gx = (36 + -12x + -12x + 4x2 + (-3 * x2 + x * x2)) gx = (36 + -12x + -12x + 4x2 + (-3x2 + x3)) Combine like terms: -12x + -12x = -24x gx = (36 + -24x + 4x2 + -3x2 + x3) Combine like terms: 4x2 + -3x2 = 1x2 gx = (36 + -24x + 1x2 + x3) Solving gx = 36 + -24x + 1x2 + 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 = 36x-1 + -24 + x + x2 Simplifying g = 36x-1 + -24 + x + x2 Reorder the terms: g = -24 + 36x-1 + x + x2
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