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Simplifying P(x) = x2 + 4x Multiply P * x xP = x2 + 4x Reorder the terms: xP = 4x + x2 Solving xP = 4x + x2 Solving for variable 'x'. Reorder the terms: -4x + xP + -1x2 = 4x + x2 + -4x + -1x2 Reorder the terms: -4x + xP + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -4x + xP + -1x2 = 0 + x2 + -1x2 -4x + xP + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4x + xP + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + P + -1x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-4 + P + -1x)' equal to zero and attempt to solve: Simplifying -4 + P + -1x = 0 Solving -4 + P + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + P + 4 + -1x = 0 + 4 Reorder the terms: -4 + 4 + P + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + P + -1x = 0 + 4 P + -1x = 0 + 4 Combine like terms: 0 + 4 = 4 P + -1x = 4 Add '-1P' to each side of the equation. P + -1P + -1x = 4 + -1P Combine like terms: P + -1P = 0 0 + -1x = 4 + -1P -1x = 4 + -1P Divide each side by '-1'. x = -4 + P Simplifying x = -4 + PSolution
x = {0, -4 + P}
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