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Simplifying f(x) = (2x + -1)(x2 + 3)(x2 + -5) Multiply f * x fx = (2x + -1)(x2 + 3)(x2 + -5) Reorder the terms: fx = (-1 + 2x)(x2 + 3)(x2 + -5) Reorder the terms: fx = (-1 + 2x)(3 + x2)(x2 + -5) Reorder the terms: fx = (-1 + 2x)(3 + x2)(-5 + x2) Multiply (-1 + 2x) * (3 + x2) fx = (-1(3 + x2) + 2x * (3 + x2))(-5 + x2) fx = ((3 * -1 + x2 * -1) + 2x * (3 + x2))(-5 + x2) fx = ((-3 + -1x2) + 2x * (3 + x2))(-5 + x2) fx = (-3 + -1x2 + (3 * 2x + x2 * 2x))(-5 + x2) fx = (-3 + -1x2 + (6x + 2x3))(-5 + x2) Reorder the terms: fx = (-3 + 6x + -1x2 + 2x3)(-5 + x2) fx = (-3 + 6x + -1x2 + 2x3)(-5 + x2) Multiply (-3 + 6x + -1x2 + 2x3) * (-5 + x2) fx = (-3(-5 + x2) + 6x * (-5 + x2) + -1x2 * (-5 + x2) + 2x3 * (-5 + x2)) fx = ((-5 * -3 + x2 * -3) + 6x * (-5 + x2) + -1x2 * (-5 + x2) + 2x3 * (-5 + x2)) fx = ((15 + -3x2) + 6x * (-5 + x2) + -1x2 * (-5 + x2) + 2x3 * (-5 + x2)) fx = (15 + -3x2 + (-5 * 6x + x2 * 6x) + -1x2 * (-5 + x2) + 2x3 * (-5 + x2)) fx = (15 + -3x2 + (-30x + 6x3) + -1x2 * (-5 + x2) + 2x3 * (-5 + x2)) fx = (15 + -3x2 + -30x + 6x3 + (-5 * -1x2 + x2 * -1x2) + 2x3 * (-5 + x2)) fx = (15 + -3x2 + -30x + 6x3 + (5x2 + -1x4) + 2x3 * (-5 + x2)) fx = (15 + -3x2 + -30x + 6x3 + 5x2 + -1x4 + (-5 * 2x3 + x2 * 2x3)) fx = (15 + -3x2 + -30x + 6x3 + 5x2 + -1x4 + (-10x3 + 2x5)) Reorder the terms: fx = (15 + -30x + -3x2 + 5x2 + 6x3 + -10x3 + -1x4 + 2x5) Combine like terms: -3x2 + 5x2 = 2x2 fx = (15 + -30x + 2x2 + 6x3 + -10x3 + -1x4 + 2x5) Combine like terms: 6x3 + -10x3 = -4x3 fx = (15 + -30x + 2x2 + -4x3 + -1x4 + 2x5) Solving fx = 15 + -30x + 2x2 + -4x3 + -1x4 + 2x5 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 15x-1 + -30 + 2x + -4x2 + -1x3 + 2x4 Simplifying f = 15x-1 + -30 + 2x + -4x2 + -1x3 + 2x4 Reorder the terms: f = -30 + 15x-1 + 2x + -4x2 + -1x3 + 2x4
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