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Simplifying 15p6 + -5p4 + -10p2 = 0 Reorder the terms: -10p2 + -5p4 + 15p6 = 0 Solving -10p2 + -5p4 + 15p6 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p2'. 5p2(-2 + -1p2 + 3p4) = 0 Factor a trinomial. 5p2((-2 + -3p2)(1 + -1p2)) = 0 Factor a difference between two squares. 5p2((-2 + -3p2)((1 + p)(1 + -1p))) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(-2 + -3p2)' equal to zero and attempt to solve: Simplifying -2 + -3p2 = 0 Solving -2 + -3p2 = 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 + -3p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3p2 = 0 + 2 -3p2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3p2 = 2 Divide each side by '-3'. p2 = -0.6666666667 Simplifying p2 = -0.6666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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 4
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, -1, 1}
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