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Simplifying f(x) = 2(x + 4)(x + 1)(x + -1) Multiply f * x fx = 2(x + 4)(x + 1)(x + -1) Reorder the terms: fx = 2(4 + x)(x + 1)(x + -1) Reorder the terms: fx = 2(4 + x)(1 + x)(x + -1) Reorder the terms: fx = 2(4 + x)(1 + x)(-1 + x) Multiply (4 + x) * (1 + x) fx = 2(4(1 + x) + x(1 + x))(-1 + x) fx = 2((1 * 4 + x * 4) + x(1 + x))(-1 + x) fx = 2((4 + 4x) + x(1 + x))(-1 + x) fx = 2(4 + 4x + (1 * x + x * x))(-1 + x) fx = 2(4 + 4x + (1x + x2))(-1 + x) Combine like terms: 4x + 1x = 5x fx = 2(4 + 5x + x2)(-1 + x) Multiply (4 + 5x + x2) * (-1 + x) fx = 2(4(-1 + x) + 5x * (-1 + x) + x2(-1 + x)) fx = 2((-1 * 4 + x * 4) + 5x * (-1 + x) + x2(-1 + x)) fx = 2((-4 + 4x) + 5x * (-1 + x) + x2(-1 + x)) fx = 2(-4 + 4x + (-1 * 5x + x * 5x) + x2(-1 + x)) fx = 2(-4 + 4x + (-5x + 5x2) + x2(-1 + x)) fx = 2(-4 + 4x + -5x + 5x2 + (-1 * x2 + x * x2)) fx = 2(-4 + 4x + -5x + 5x2 + (-1x2 + x3)) Combine like terms: 4x + -5x = -1x fx = 2(-4 + -1x + 5x2 + -1x2 + x3) Combine like terms: 5x2 + -1x2 = 4x2 fx = 2(-4 + -1x + 4x2 + x3) fx = (-4 * 2 + -1x * 2 + 4x2 * 2 + x3 * 2) fx = (-8 + -2x + 8x2 + 2x3) Solving fx = -8 + -2x + 8x2 + 2x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -8x-1 + -2 + 8x + 2x2 Simplifying f = -8x-1 + -2 + 8x + 2x2 Reorder the terms: f = -2 + -8x-1 + 8x + 2x2
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