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Simplifying f(x) = (2x + 3)(x + -4)(x + 5) Multiply f * x fx = (2x + 3)(x + -4)(x + 5) Reorder the terms: fx = (3 + 2x)(x + -4)(x + 5) Reorder the terms: fx = (3 + 2x)(-4 + x)(x + 5) Reorder the terms: fx = (3 + 2x)(-4 + x)(5 + x) Multiply (3 + 2x) * (-4 + x) fx = (3(-4 + x) + 2x * (-4 + x))(5 + x) fx = ((-4 * 3 + x * 3) + 2x * (-4 + x))(5 + x) fx = ((-12 + 3x) + 2x * (-4 + x))(5 + x) fx = (-12 + 3x + (-4 * 2x + x * 2x))(5 + x) fx = (-12 + 3x + (-8x + 2x2))(5 + x) Combine like terms: 3x + -8x = -5x fx = (-12 + -5x + 2x2)(5 + x) Multiply (-12 + -5x + 2x2) * (5 + x) fx = (-12(5 + x) + -5x * (5 + x) + 2x2 * (5 + x)) fx = ((5 * -12 + x * -12) + -5x * (5 + x) + 2x2 * (5 + x)) fx = ((-60 + -12x) + -5x * (5 + x) + 2x2 * (5 + x)) fx = (-60 + -12x + (5 * -5x + x * -5x) + 2x2 * (5 + x)) fx = (-60 + -12x + (-25x + -5x2) + 2x2 * (5 + x)) fx = (-60 + -12x + -25x + -5x2 + (5 * 2x2 + x * 2x2)) fx = (-60 + -12x + -25x + -5x2 + (10x2 + 2x3)) Combine like terms: -12x + -25x = -37x fx = (-60 + -37x + -5x2 + 10x2 + 2x3) Combine like terms: -5x2 + 10x2 = 5x2 fx = (-60 + -37x + 5x2 + 2x3) Solving fx = -60 + -37x + 5x2 + 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 = -60x-1 + -37 + 5x + 2x2 Simplifying f = -60x-1 + -37 + 5x + 2x2 Reorder the terms: f = -37 + -60x-1 + 5x + 2x2
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