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Simplifying (3x + -6) * p(x) = 3x4 + -6x3 + 6x2 + 3x + -30 Reorder the terms: (-6 + 3x) * p(x) = 3x4 + -6x3 + 6x2 + 3x + -30 Reorder the terms for easier multiplication: p * x(-6 + 3x) = 3x4 + -6x3 + 6x2 + 3x + -30 Multiply p * x px(-6 + 3x) = 3x4 + -6x3 + 6x2 + 3x + -30 (-6 * px + 3x * px) = 3x4 + -6x3 + 6x2 + 3x + -30 (-6px + 3px2) = 3x4 + -6x3 + 6x2 + 3x + -30 Reorder the terms: -6px + 3px2 = -30 + 3x + 6x2 + -6x3 + 3x4 Solving -6px + 3px2 = -30 + 3x + 6x2 + -6x3 + 3x4 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Reorder the terms: 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = -30 + 3x + 6x2 + -6x3 + 3x4 + 30 + -3x + -6x2 + 6x3 + -3x4 Reorder the terms: 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = -30 + 30 + 3x + -3x + 6x2 + -6x2 + -6x3 + 6x3 + 3x4 + -3x4 Combine like terms: -30 + 30 = 0 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 0 + 3x + -3x + 6x2 + -6x2 + -6x3 + 6x3 + 3x4 + -3x4 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 3x + -3x + 6x2 + -6x2 + -6x3 + 6x3 + 3x4 + -3x4 Combine like terms: 3x + -3x = 0 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 0 + 6x2 + -6x2 + -6x3 + 6x3 + 3x4 + -3x4 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 6x2 + -6x2 + -6x3 + 6x3 + 3x4 + -3x4 Combine like terms: 6x2 + -6x2 = 0 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 0 + -6x3 + 6x3 + 3x4 + -3x4 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = -6x3 + 6x3 + 3x4 + -3x4 Combine like terms: -6x3 + 6x3 = 0 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 0 + 3x4 + -3x4 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 3x4 + -3x4 Combine like terms: 3x4 + -3x4 = 0 30 + -6px + 3px2 + -3x + -6x2 + 6x3 + -3x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4)' equal to zero and attempt to solve: Simplifying 10 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = 0 Solving 10 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -2px + px2 + -1x + -2x2 + 2x3 + -10 + -1x4 = 0 + -10 Reorder the terms: 10 + -10 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = 0 + -10 -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = 0 + -10 Combine like terms: 0 + -10 = -10 -2px + px2 + -1x + -2x2 + 2x3 + -1x4 = -10 Add 'x' to each side of the equation. -2px + px2 + -1x + -2x2 + 2x3 + x + -1x4 = -10 + x Reorder the terms: -2px + px2 + -1x + x + -2x2 + 2x3 + -1x4 = -10 + x Combine like terms: -1x + x = 0 -2px + px2 + 0 + -2x2 + 2x3 + -1x4 = -10 + x -2px + px2 + -2x2 + 2x3 + -1x4 = -10 + x Add '2x2' to each side of the equation. -2px + px2 + -2x2 + 2x3 + 2x2 + -1x4 = -10 + x + 2x2 Reorder the terms: -2px + px2 + -2x2 + 2x2 + 2x3 + -1x4 = -10 + x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -2px + px2 + 0 + 2x3 + -1x4 = -10 + x + 2x2 -2px + px2 + 2x3 + -1x4 = -10 + x + 2x2 Add '-2x3' to each side of the equation. -2px + px2 + 2x3 + -2x3 + -1x4 = -10 + x + 2x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -2px + px2 + 0 + -1x4 = -10 + x + 2x2 + -2x3 -2px + px2 + -1x4 = -10 + x + 2x2 + -2x3 Add 'x4' to each side of the equation. -2px + px2 + -1x4 + x4 = -10 + x + 2x2 + -2x3 + x4 Combine like terms: -1x4 + x4 = 0 -2px + px2 + 0 = -10 + x + 2x2 + -2x3 + x4 -2px + px2 = -10 + x + 2x2 + -2x3 + x4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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