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Simplifying f(x) = (x + 5)(x + 2)(x + 5i) Multiply f * x fx = (x + 5)(x + 2)(x + 5i) Reorder the terms: fx = (5 + x)(x + 2)(x + 5i) Reorder the terms: fx = (5 + x)(2 + x)(x + 5i) Reorder the terms: fx = (5 + x)(2 + x)(5i + x) Multiply (5 + x) * (2 + x) fx = (5(2 + x) + x(2 + x))(5i + x) fx = ((2 * 5 + x * 5) + x(2 + x))(5i + x) fx = ((10 + 5x) + x(2 + x))(5i + x) fx = (10 + 5x + (2 * x + x * x))(5i + x) fx = (10 + 5x + (2x + x2))(5i + x) Combine like terms: 5x + 2x = 7x fx = (10 + 7x + x2)(5i + x) Multiply (10 + 7x + x2) * (5i + x) fx = (10(5i + x) + 7x * (5i + x) + x2(5i + x)) fx = ((5i * 10 + x * 10) + 7x * (5i + x) + x2(5i + x)) fx = ((50i + 10x) + 7x * (5i + x) + x2(5i + x)) fx = (50i + 10x + (5i * 7x + x * 7x) + x2(5i + x)) fx = (50i + 10x + (35ix + 7x2) + x2(5i + x)) fx = (50i + 10x + 35ix + 7x2 + (5i * x2 + x * x2)) fx = (50i + 10x + 35ix + 7x2 + (5ix2 + x3)) Reorder the terms: fx = (50i + 35ix + 5ix2 + 10x + 7x2 + x3) fx = (50i + 35ix + 5ix2 + 10x + 7x2 + x3) Solving fx = 50i + 35ix + 5ix2 + 10x + 7x2 + 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 = 50ix-1 + 35i + 5ix + 10 + 7x + x2 Simplifying f = 50ix-1 + 35i + 5ix + 10 + 7x + x2 Reorder the terms: f = 10 + 35i + 50ix-1 + 5ix + 7x + x2
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