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Simplifying f(x) = x(x + 2)(x + -2)(3x2 + -4) Multiply f * x fx = x(x + 2)(x + -2)(3x2 + -4) Reorder the terms: fx = x(2 + x)(x + -2)(3x2 + -4) Reorder the terms: fx = x(2 + x)(-2 + x)(3x2 + -4) Reorder the terms: fx = x(2 + x)(-2 + x)(-4 + 3x2) Multiply (2 + x) * (-2 + x) fx = x(2(-2 + x) + x(-2 + x))(-4 + 3x2) fx = x((-2 * 2 + x * 2) + x(-2 + x))(-4 + 3x2) fx = x((-4 + 2x) + x(-2 + x))(-4 + 3x2) fx = x(-4 + 2x + (-2 * x + x * x))(-4 + 3x2) fx = x(-4 + 2x + (-2x + x2))(-4 + 3x2) Combine like terms: 2x + -2x = 0 fx = x(-4 + 0 + x2)(-4 + 3x2) fx = x(-4 + x2)(-4 + 3x2) Multiply (-4 + x2) * (-4 + 3x2) fx = x(-4(-4 + 3x2) + x2(-4 + 3x2)) fx = x((-4 * -4 + 3x2 * -4) + x2(-4 + 3x2)) fx = x((16 + -12x2) + x2(-4 + 3x2)) fx = x(16 + -12x2 + (-4 * x2 + 3x2 * x2)) fx = x(16 + -12x2 + (-4x2 + 3x4)) Combine like terms: -12x2 + -4x2 = -16x2 fx = x(16 + -16x2 + 3x4) fx = (16 * x + -16x2 * x + 3x4 * x) fx = (16x + -16x3 + 3x5) Solving fx = 16x + -16x3 + 3x5 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 16 + -16x2 + 3x4 Simplifying f = 16 + -16x2 + 3x4
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