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Simplifying -4p5 + -16p + 20p3 = 0 Reorder the terms: -16p + 20p3 + -4p5 = 0 Solving -16p + 20p3 + -4p5 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4p'. 4p(-4 + 5p2 + -1p4) = 0 Factor a trinomial. 4p((-4 + p2)(1 + -1p2)) = 0 Factor a difference between two squares. 4p(((2 + p)(-2 + p))(1 + -1p2)) = 0 Factor a difference between two squares. 4p(((1 + p)(1 + -1p))(2 + p)(-2 + p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Subproblem 3
Set the factor '(-2 + p)' equal to zero and attempt to solve: Simplifying -2 + p = 0 Solving -2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + p = 0 + 2 p = 0 + 2 Combine like terms: 0 + 2 = 2 p = 2 Simplifying p = 2Subproblem 4
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Subproblem 5
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {0, -2, 2, -1, 1}
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