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Simplifying f(x) = [x + -1(3 + -3i)][x + -1(3 + 3i)](x + 2)(x + -1) Multiply f * x fx = [x + -1(3 + -3i)][x + -1(3 + 3i)](x + 2)(x + -1) fx = [x + (3 * -1 + -3i * -1)][x + -1(3 + 3i)](x + 2)(x + -1) fx = [x + (-3 + 3i)][x + -1(3 + 3i)](x + 2)(x + -1) Reorder the terms: fx = [-3 + 3i + x][x + -1(3 + 3i)](x + 2)(x + -1) fx = [-3 + 3i + x][x + (3 * -1 + 3i * -1)](x + 2)(x + -1) fx = [-3 + 3i + x][x + (-3 + -3i)](x + 2)(x + -1) Reorder the terms: fx = [-3 + 3i + x][-3 + -3i + x](x + 2)(x + -1) Reorder the terms: fx = [-3 + 3i + x][-3 + -3i + x](2 + x)(x + -1) Reorder the terms: fx = [-3 + 3i + x][-3 + -3i + x](2 + x)(-1 + x) Multiply [-3 + 3i + x] * [-3 + -3i + x] fx = [-3[-3 + -3i + x] + 3i * [-3 + -3i + x] + x[-3 + -3i + x]](2 + x)(-1 + x) fx = [[-3 * -3 + -3i * -3 + x * -3] + 3i * [-3 + -3i + x] + x[-3 + -3i + x]](2 + x)(-1 + x) fx = [[9 + 9i + -3x] + 3i * [-3 + -3i + x] + x[-3 + -3i + x]](2 + x)(-1 + x) fx = [9 + 9i + -3x + [-3 * 3i + -3i * 3i + x * 3i] + x[-3 + -3i + x]](2 + x)(-1 + x) Reorder the terms: fx = [9 + 9i + -3x + [-9i + 3ix + -9i2] + x[-3 + -3i + x]](2 + x)(-1 + x) fx = [9 + 9i + -3x + [-9i + 3ix + -9i2] + x[-3 + -3i + x]](2 + x)(-1 + x) fx = [9 + 9i + -3x + -9i + 3ix + -9i2 + [-3 * x + -3i * x + x * x]](2 + x)(-1 + x) Reorder the terms: fx = [9 + 9i + -3x + -9i + 3ix + -9i2 + [-3ix + -3x + x2]](2 + x)(-1 + x) fx = [9 + 9i + -3x + -9i + 3ix + -9i2 + [-3ix + -3x + x2]](2 + x)(-1 + x) Reorder the terms: fx = [9 + 9i + -9i + 3ix + -3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) Combine like terms: 9i + -9i = 0 fx = [9 + 0 + 3ix + -3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) fx = [9 + 3ix + -3ix + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) Combine like terms: 3ix + -3ix = 0 fx = [9 + 0 + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) fx = [9 + -9i2 + -3x + -3x + x2](2 + x)(-1 + x) Combine like terms: -3x + -3x = -6x fx = [9 + -9i2 + -6x + x2](2 + x)(-1 + x) Multiply [9 + -9i2 + -6x + x2] * (2 + x) fx = [9(2 + x) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) fx = [(2 * 9 + x * 9) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) fx = [(18 + 9x) + -9i2 * (2 + x) + -6x * (2 + x) + x2(2 + x)](-1 + x) fx = [18 + 9x + (2 * -9i2 + x * -9i2) + -6x * (2 + x) + x2(2 + x)](-1 + x) fx = [18 + 9x + (-18i2 + -9i2x) + -6x * (2 + x) + x2(2 + x)](-1 + x) fx = [18 + 9x + -18i2 + -9i2x + (2 * -6x + x * -6x) + x2(2 + x)](-1 + x) fx = [18 + 9x + -18i2 + -9i2x + (-12x + -6x2) + x2(2 + x)](-1 + x) fx = [18 + 9x + -18i2 + -9i2x + -12x + -6x2 + (2 * x2 + x * x2)](-1 + x) fx = [18 + 9x + -18i2 + -9i2x + -12x + -6x2 + (2x2 + x3)](-1 + x) Reorder the terms: fx = [18 + -18i2 + -9i2x + 9x + -12x + -6x2 + 2x2 + x3](-1 + x) Combine like terms: 9x + -12x = -3x fx = [18 + -18i2 + -9i2x + -3x + -6x2 + 2x2 + x3](-1 + x) Combine like terms: -6x2 + 2x2 = -4x2 fx = [18 + -18i2 + -9i2x + -3x + -4x2 + x3](-1 + x) Multiply [18 + -18i2 + -9i2x + -3x + -4x2 + x3] * (-1 + x) fx = [18(-1 + x) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [(-1 * 18 + x * 18) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [(-18 + 18x) + -18i2 * (-1 + x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + (-1 * -18i2 + x * -18i2) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + (18i2 + -18i2x) + -9i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + (-1 * -9i2x + x * -9i2x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + (9i2x + -9i2x2) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + (-1 * -3x + x * -3x) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + (3x + -3x2) + -4x2 * (-1 + x) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + (-1 * -4x2 + x * -4x2) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + (4x2 + -4x3) + x3(-1 + x)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1 * x3 + x * x3)] fx = [-18 + 18x + 18i2 + -18i2x + 9i2x + -9i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1x3 + x4)] Reorder the terms: fx = [-18 + 18i2 + -18i2x + 9i2x + -9i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4] Combine like terms: -18i2x + 9i2x = -9i2x fx = [-18 + 18i2 + -9i2x + -9i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4] Combine like terms: 18x + 3x = 21x fx = [-18 + 18i2 + -9i2x + -9i2x2 + 21x + -3x2 + 4x2 + -4x3 + -1x3 + x4] Combine like terms: -3x2 + 4x2 = 1x2 fx = [-18 + 18i2 + -9i2x + -9i2x2 + 21x + 1x2 + -4x3 + -1x3 + x4] Combine like terms: -4x3 + -1x3 = -5x3 fx = [-18 + 18i2 + -9i2x + -9i2x2 + 21x + 1x2 + -5x3 + x4] Solving fx = -18 + 18i2 + -9i2x + -9i2x2 + 21x + 1x2 + -5x3 + x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -18x-1 + 18i2x-1 + -9i2 + -9i2x + 21 + x + -5x2 + x3 Simplifying f = -18x-1 + 18i2x-1 + -9i2 + -9i2x + 21 + x + -5x2 + x3 Reorder the terms: f = 21 + -9i2 + 18i2x-1 + -9i2x + -18x-1 + x + -5x2 + x3
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