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Simplifying f(x) = (x + -3)(x + 2)(x + 5) Multiply f * x fx = (x + -3)(x + 2)(x + 5) Reorder the terms: fx = (-3 + x)(x + 2)(x + 5) Reorder the terms: fx = (-3 + x)(2 + x)(x + 5) Reorder the terms: fx = (-3 + x)(2 + x)(5 + x) Multiply (-3 + x) * (2 + x) fx = (-3(2 + x) + x(2 + x))(5 + x) fx = ((2 * -3 + x * -3) + x(2 + x))(5 + x) fx = ((-6 + -3x) + x(2 + x))(5 + x) fx = (-6 + -3x + (2 * x + x * x))(5 + x) fx = (-6 + -3x + (2x + x2))(5 + x) Combine like terms: -3x + 2x = -1x fx = (-6 + -1x + x2)(5 + x) Multiply (-6 + -1x + x2) * (5 + x) fx = (-6(5 + x) + -1x * (5 + x) + x2(5 + x)) fx = ((5 * -6 + x * -6) + -1x * (5 + x) + x2(5 + x)) fx = ((-30 + -6x) + -1x * (5 + x) + x2(5 + x)) fx = (-30 + -6x + (5 * -1x + x * -1x) + x2(5 + x)) fx = (-30 + -6x + (-5x + -1x2) + x2(5 + x)) fx = (-30 + -6x + -5x + -1x2 + (5 * x2 + x * x2)) fx = (-30 + -6x + -5x + -1x2 + (5x2 + x3)) Combine like terms: -6x + -5x = -11x fx = (-30 + -11x + -1x2 + 5x2 + x3) Combine like terms: -1x2 + 5x2 = 4x2 fx = (-30 + -11x + 4x2 + x3) Solving fx = -30 + -11x + 4x2 + 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 = -30x-1 + -11 + 4x + x2 Simplifying f = -30x-1 + -11 + 4x + x2 Reorder the terms: f = -11 + -30x-1 + 4x + x2
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