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Simplifying f(x) = x(2x + -1)(x + -1)(x + 1) Multiply f * x fx = x(2x + -1)(x + -1)(x + 1) Reorder the terms: fx = x(-1 + 2x)(x + -1)(x + 1) Reorder the terms: fx = x(-1 + 2x)(-1 + x)(x + 1) Reorder the terms: fx = x(-1 + 2x)(-1 + x)(1 + x) Multiply (-1 + 2x) * (-1 + x) fx = x(-1(-1 + x) + 2x * (-1 + x))(1 + x) fx = x((-1 * -1 + x * -1) + 2x * (-1 + x))(1 + x) fx = x((1 + -1x) + 2x * (-1 + x))(1 + x) fx = x(1 + -1x + (-1 * 2x + x * 2x))(1 + x) fx = x(1 + -1x + (-2x + 2x2))(1 + x) Combine like terms: -1x + -2x = -3x fx = x(1 + -3x + 2x2)(1 + x) Multiply (1 + -3x + 2x2) * (1 + x) fx = x(1(1 + x) + -3x * (1 + x) + 2x2 * (1 + x)) fx = x((1 * 1 + x * 1) + -3x * (1 + x) + 2x2 * (1 + x)) fx = x((1 + 1x) + -3x * (1 + x) + 2x2 * (1 + x)) fx = x(1 + 1x + (1 * -3x + x * -3x) + 2x2 * (1 + x)) fx = x(1 + 1x + (-3x + -3x2) + 2x2 * (1 + x)) fx = x(1 + 1x + -3x + -3x2 + (1 * 2x2 + x * 2x2)) fx = x(1 + 1x + -3x + -3x2 + (2x2 + 2x3)) Combine like terms: 1x + -3x = -2x fx = x(1 + -2x + -3x2 + 2x2 + 2x3) Combine like terms: -3x2 + 2x2 = -1x2 fx = x(1 + -2x + -1x2 + 2x3) fx = (1 * x + -2x * x + -1x2 * x + 2x3 * x) fx = (1x + -2x2 + -1x3 + 2x4) Solving fx = 1x + -2x2 + -1x3 + 2x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 1 + -2x + -1x2 + 2x3 Simplifying f = 1 + -2x + -1x2 + 2x3
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