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Simplifying P(x) = (x + -2)(x + -3)(x + -1)(x + -3) Multiply P * x xP = (x + -2)(x + -3)(x + -1)(x + -3) Reorder the terms: xP = (-2 + x)(x + -3)(x + -1)(x + -3) Reorder the terms: xP = (-2 + x)(-3 + x)(x + -1)(x + -3) Reorder the terms: xP = (-2 + x)(-3 + x)(-1 + x)(x + -3) Reorder the terms: xP = (-2 + x)(-3 + x)(-1 + x)(-3 + x) Multiply (-2 + x) * (-3 + x) xP = (-2(-3 + x) + x(-3 + x))(-1 + x)(-3 + x) xP = ((-3 * -2 + x * -2) + x(-3 + x))(-1 + x)(-3 + x) xP = ((6 + -2x) + x(-3 + x))(-1 + x)(-3 + x) xP = (6 + -2x + (-3 * x + x * x))(-1 + x)(-3 + x) xP = (6 + -2x + (-3x + x2))(-1 + x)(-3 + x) Combine like terms: -2x + -3x = -5x xP = (6 + -5x + x2)(-1 + x)(-3 + x) Multiply (6 + -5x + x2) * (-1 + x) xP = (6(-1 + x) + -5x * (-1 + x) + x2(-1 + x))(-3 + x) xP = ((-1 * 6 + x * 6) + -5x * (-1 + x) + x2(-1 + x))(-3 + x) xP = ((-6 + 6x) + -5x * (-1 + x) + x2(-1 + x))(-3 + x) xP = (-6 + 6x + (-1 * -5x + x * -5x) + x2(-1 + x))(-3 + x) xP = (-6 + 6x + (5x + -5x2) + x2(-1 + x))(-3 + x) xP = (-6 + 6x + 5x + -5x2 + (-1 * x2 + x * x2))(-3 + x) xP = (-6 + 6x + 5x + -5x2 + (-1x2 + x3))(-3 + x) Combine like terms: 6x + 5x = 11x xP = (-6 + 11x + -5x2 + -1x2 + x3)(-3 + x) Combine like terms: -5x2 + -1x2 = -6x2 xP = (-6 + 11x + -6x2 + x3)(-3 + x) Multiply (-6 + 11x + -6x2 + x3) * (-3 + x) xP = (-6(-3 + x) + 11x * (-3 + x) + -6x2 * (-3 + x) + x3(-3 + x)) xP = ((-3 * -6 + x * -6) + 11x * (-3 + x) + -6x2 * (-3 + x) + x3(-3 + x)) xP = ((18 + -6x) + 11x * (-3 + x) + -6x2 * (-3 + x) + x3(-3 + x)) xP = (18 + -6x + (-3 * 11x + x * 11x) + -6x2 * (-3 + x) + x3(-3 + x)) xP = (18 + -6x + (-33x + 11x2) + -6x2 * (-3 + x) + x3(-3 + x)) xP = (18 + -6x + -33x + 11x2 + (-3 * -6x2 + x * -6x2) + x3(-3 + x)) xP = (18 + -6x + -33x + 11x2 + (18x2 + -6x3) + x3(-3 + x)) xP = (18 + -6x + -33x + 11x2 + 18x2 + -6x3 + (-3 * x3 + x * x3)) xP = (18 + -6x + -33x + 11x2 + 18x2 + -6x3 + (-3x3 + x4)) Combine like terms: -6x + -33x = -39x xP = (18 + -39x + 11x2 + 18x2 + -6x3 + -3x3 + x4) Combine like terms: 11x2 + 18x2 = 29x2 xP = (18 + -39x + 29x2 + -6x3 + -3x3 + x4) Combine like terms: -6x3 + -3x3 = -9x3 xP = (18 + -39x + 29x2 + -9x3 + x4) Solving xP = 18 + -39x + 29x2 + -9x3 + x4 Solving for variable 'x'. Reorder the terms: -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 18 + -39x + 29x2 + -9x3 + x4 + -18 + 39x + -29x2 + 9x3 + -1x4 Reorder the terms: -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 18 + -18 + -39x + 39x + 29x2 + -29x2 + -9x3 + 9x3 + x4 + -1x4 Combine like terms: 18 + -18 = 0 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 0 + -39x + 39x + 29x2 + -29x2 + -9x3 + 9x3 + x4 + -1x4 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = -39x + 39x + 29x2 + -29x2 + -9x3 + 9x3 + x4 + -1x4 Combine like terms: -39x + 39x = 0 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 0 + 29x2 + -29x2 + -9x3 + 9x3 + x4 + -1x4 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 29x2 + -29x2 + -9x3 + 9x3 + x4 + -1x4 Combine like terms: 29x2 + -29x2 = 0 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 0 + -9x3 + 9x3 + x4 + -1x4 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = -9x3 + 9x3 + x4 + -1x4 Combine like terms: -9x3 + 9x3 = 0 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 0 + x4 + -1x4 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -18 + 39x + xP + -29x2 + 9x3 + -1x4 = 0 The solution to this equation could not be determined.
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