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Simplifying P(x) = (x + 4)[x + -1(2 + 5i)][x + -1(2 + -5i)] Multiply P * x xP = (x + 4)[x + -1(2 + 5i)][x + -1(2 + -5i)] Reorder the terms: xP = (4 + x)[x + -1(2 + 5i)][x + -1(2 + -5i)] xP = (4 + x)[x + (2 * -1 + 5i * -1)][x + -1(2 + -5i)] xP = (4 + x)[x + (-2 + -5i)][x + -1(2 + -5i)] Reorder the terms: xP = (4 + x)[-2 + -5i + x][x + -1(2 + -5i)] xP = (4 + x)[-2 + -5i + x][x + (2 * -1 + -5i * -1)] xP = (4 + x)[-2 + -5i + x][x + (-2 + 5i)] Reorder the terms: xP = (4 + x)[-2 + -5i + x][-2 + 5i + x] Multiply (4 + x) * [-2 + -5i + x] xP = (4[-2 + -5i + x] + x[-2 + -5i + x])[-2 + 5i + x] xP = ([-2 * 4 + -5i * 4 + x * 4] + x[-2 + -5i + x])[-2 + 5i + x] xP = ([-8 + -20i + 4x] + x[-2 + -5i + x])[-2 + 5i + x] xP = (-8 + -20i + 4x + [-2 * x + -5i * x + x * x])[-2 + 5i + x] Reorder the terms: xP = (-8 + -20i + 4x + [-5ix + -2x + x2])[-2 + 5i + x] xP = (-8 + -20i + 4x + [-5ix + -2x + x2])[-2 + 5i + x] Reorder the terms: xP = (-8 + -20i + -5ix + 4x + -2x + x2)[-2 + 5i + x] Combine like terms: 4x + -2x = 2x xP = (-8 + -20i + -5ix + 2x + x2)[-2 + 5i + x] Multiply (-8 + -20i + -5ix + 2x + x2) * [-2 + 5i + x] xP = (-8[-2 + 5i + x] + -20i * [-2 + 5i + x] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = ([-2 * -8 + 5i * -8 + x * -8] + -20i * [-2 + 5i + x] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = ([16 + -40i + -8x] + -20i * [-2 + 5i + x] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + [-2 * -20i + 5i * -20i + x * -20i] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) Reorder the terms: xP = (16 + -40i + -8x + [40i + -20ix + -100i2] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + [40i + -20ix + -100i2] + -5ix * [-2 + 5i + x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + [-2 * -5ix + 5i * -5ix + x * -5ix] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) Reorder the terms: xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + [10ix + -5ix2 + -25i2x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + [10ix + -5ix2 + -25i2x] + 2x * [-2 + 5i + x] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + [-2 * 2x + 5i * 2x + x * 2x] + x2[-2 + 5i + x]) Reorder the terms: xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + [10ix + -4x + 2x2] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + [10ix + -4x + 2x2] + x2[-2 + 5i + x]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + 10ix + -4x + 2x2 + [-2 * x2 + 5i * x2 + x * x2]) Reorder the terms: xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + 10ix + -4x + 2x2 + [5ix2 + -2x2 + x3]) xP = (16 + -40i + -8x + 40i + -20ix + -100i2 + 10ix + -5ix2 + -25i2x + 10ix + -4x + 2x2 + [5ix2 + -2x2 + x3]) Reorder the terms: xP = (16 + -40i + 40i + -20ix + 10ix + 10ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) Combine like terms: -40i + 40i = 0 xP = (16 + 0 + -20ix + 10ix + 10ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) xP = (16 + -20ix + 10ix + 10ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) Combine like terms: -20ix + 10ix = -10ix xP = (16 + -10ix + 10ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) Combine like terms: -10ix + 10ix = 0 xP = (16 + 0 + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) xP = (16 + -5ix2 + 5ix2 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) Combine like terms: -5ix2 + 5ix2 = 0 xP = (16 + 0 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) xP = (16 + -100i2 + -25i2x + -8x + -4x + 2x2 + -2x2 + x3) Combine like terms: -8x + -4x = -12x xP = (16 + -100i2 + -25i2x + -12x + 2x2 + -2x2 + x3) Combine like terms: 2x2 + -2x2 = 0 xP = (16 + -100i2 + -25i2x + -12x + 0 + x3) xP = (16 + -100i2 + -25i2x + -12x + x3) Solving xP = 16 + -100i2 + -25i2x + -12x + x3 Solving for variable 'x'. Reorder the terms: -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 16 + -100i2 + -25i2x + -12x + x3 + -16 + 100i2 + 25i2x + 12x + -1x3 Reorder the terms: -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 16 + -16 + -100i2 + 100i2 + -25i2x + 25i2x + -12x + 12x + x3 + -1x3 Combine like terms: 16 + -16 = 0 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 0 + -100i2 + 100i2 + -25i2x + 25i2x + -12x + 12x + x3 + -1x3 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = -100i2 + 100i2 + -25i2x + 25i2x + -12x + 12x + x3 + -1x3 Combine like terms: -100i2 + 100i2 = 0 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 0 + -25i2x + 25i2x + -12x + 12x + x3 + -1x3 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = -25i2x + 25i2x + -12x + 12x + x3 + -1x3 Combine like terms: -25i2x + 25i2x = 0 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 0 + -12x + 12x + x3 + -1x3 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = -12x + 12x + x3 + -1x3 Combine like terms: -12x + 12x = 0 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 0 + x3 + -1x3 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -16 + 100i2 + 25i2x + 12x + xP + -1x3 = 0 The solution to this equation could not be determined.
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