P(x)=2x^4-2x^3+8x^2-8x

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Solution for P(x)=2x^4-2x^3+8x^2-8x equation:


Simplifying
P(x) = 2x4 + -2x3 + 8x2 + -8x

Multiply P * x
xP = 2x4 + -2x3 + 8x2 + -8x

Reorder the terms:
xP = -8x + 8x2 + -2x3 + 2x4

Solving
xP = -8x + 8x2 + -2x3 + 2x4

Solving for variable 'x'.

Reorder the terms:
8x + xP + -8x2 + 2x3 + -2x4 = -8x + 8x2 + -2x3 + 2x4 + 8x + -8x2 + 2x3 + -2x4

Reorder the terms:
8x + xP + -8x2 + 2x3 + -2x4 = -8x + 8x + 8x2 + -8x2 + -2x3 + 2x3 + 2x4 + -2x4

Combine like terms: -8x + 8x = 0
8x + xP + -8x2 + 2x3 + -2x4 = 0 + 8x2 + -8x2 + -2x3 + 2x3 + 2x4 + -2x4
8x + xP + -8x2 + 2x3 + -2x4 = 8x2 + -8x2 + -2x3 + 2x3 + 2x4 + -2x4

Combine like terms: 8x2 + -8x2 = 0
8x + xP + -8x2 + 2x3 + -2x4 = 0 + -2x3 + 2x3 + 2x4 + -2x4
8x + xP + -8x2 + 2x3 + -2x4 = -2x3 + 2x3 + 2x4 + -2x4

Combine like terms: -2x3 + 2x3 = 0
8x + xP + -8x2 + 2x3 + -2x4 = 0 + 2x4 + -2x4
8x + xP + -8x2 + 2x3 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
8x + xP + -8x2 + 2x3 + -2x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + P + -8x + 2x2 + -2x3) = 0

Subproblem 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 = 0

Subproblem 2

Set the factor '(8 + P + -8x + 2x2 + -2x3)' equal to zero and attempt to solve: Simplifying 8 + P + -8x + 2x2 + -2x3 = 0 Solving 8 + P + -8x + 2x2 + -2x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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