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Simplifying f(x) = (x + 2)(x + -1)(x + 5) Multiply f * x fx = (x + 2)(x + -1)(x + 5) Reorder the terms: fx = (2 + x)(x + -1)(x + 5) Reorder the terms: fx = (2 + x)(-1 + x)(x + 5) Reorder the terms: fx = (2 + x)(-1 + x)(5 + x) Multiply (2 + x) * (-1 + x) fx = (2(-1 + x) + x(-1 + x))(5 + x) fx = ((-1 * 2 + x * 2) + x(-1 + x))(5 + x) fx = ((-2 + 2x) + x(-1 + x))(5 + x) fx = (-2 + 2x + (-1 * x + x * x))(5 + x) fx = (-2 + 2x + (-1x + x2))(5 + x) Combine like terms: 2x + -1x = 1x fx = (-2 + 1x + x2)(5 + x) Multiply (-2 + 1x + x2) * (5 + x) fx = (-2(5 + x) + 1x * (5 + x) + x2(5 + x)) fx = ((5 * -2 + x * -2) + 1x * (5 + x) + x2(5 + x)) fx = ((-10 + -2x) + 1x * (5 + x) + x2(5 + x)) fx = (-10 + -2x + (5 * 1x + x * 1x) + x2(5 + x)) fx = (-10 + -2x + (5x + 1x2) + x2(5 + x)) fx = (-10 + -2x + 5x + 1x2 + (5 * x2 + x * x2)) fx = (-10 + -2x + 5x + 1x2 + (5x2 + x3)) Combine like terms: -2x + 5x = 3x fx = (-10 + 3x + 1x2 + 5x2 + x3) Combine like terms: 1x2 + 5x2 = 6x2 fx = (-10 + 3x + 6x2 + x3) Solving fx = -10 + 3x + 6x2 + 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 = -10x-1 + 3 + 6x + x2 Simplifying f = -10x-1 + 3 + 6x + x2 Reorder the terms: f = 3 + -10x-1 + 6x + x2
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