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Simplifying f(x) = (x + -1)(x + -3)(x + -5) Multiply f * x fx = (x + -1)(x + -3)(x + -5) Reorder the terms: fx = (-1 + x)(x + -3)(x + -5) Reorder the terms: fx = (-1 + x)(-3 + x)(x + -5) Reorder the terms: fx = (-1 + x)(-3 + x)(-5 + x) Multiply (-1 + x) * (-3 + x) fx = (-1(-3 + x) + x(-3 + x))(-5 + x) fx = ((-3 * -1 + x * -1) + x(-3 + x))(-5 + x) fx = ((3 + -1x) + x(-3 + x))(-5 + x) fx = (3 + -1x + (-3 * x + x * x))(-5 + x) fx = (3 + -1x + (-3x + x2))(-5 + x) Combine like terms: -1x + -3x = -4x fx = (3 + -4x + x2)(-5 + x) Multiply (3 + -4x + x2) * (-5 + x) fx = (3(-5 + x) + -4x * (-5 + x) + x2(-5 + x)) fx = ((-5 * 3 + x * 3) + -4x * (-5 + x) + x2(-5 + x)) fx = ((-15 + 3x) + -4x * (-5 + x) + x2(-5 + x)) fx = (-15 + 3x + (-5 * -4x + x * -4x) + x2(-5 + x)) fx = (-15 + 3x + (20x + -4x2) + x2(-5 + x)) fx = (-15 + 3x + 20x + -4x2 + (-5 * x2 + x * x2)) fx = (-15 + 3x + 20x + -4x2 + (-5x2 + x3)) Combine like terms: 3x + 20x = 23x fx = (-15 + 23x + -4x2 + -5x2 + x3) Combine like terms: -4x2 + -5x2 = -9x2 fx = (-15 + 23x + -9x2 + x3) Solving fx = -15 + 23x + -9x2 + x3 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 + 23 + -9x + x2 Simplifying f = -15x-1 + 23 + -9x + x2 Reorder the terms: f = 23 + -15x-1 + -9x + x2
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