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