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Simplifying 3p5 + -24p4 + -27p3 = 0 Reorder the terms: -27p3 + -24p4 + 3p5 = 0 Solving -27p3 + -24p4 + 3p5 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3p3'. 3p3(-9 + -8p + p2) = 0 Factor a trinomial. 3p3((-1 + -1p)(9 + -1p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'p3' equal to zero and attempt to solve: Simplifying p3 = 0 Solving p3 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
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 = -1Subproblem 3
Set the factor '(9 + -1p)' equal to zero and attempt to solve: Simplifying 9 + -1p = 0 Solving 9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1p = 0 + -9 -1p = 0 + -9 Combine like terms: 0 + -9 = -9 -1p = -9 Divide each side by '-1'. p = 9 Simplifying p = 9Solution
p = {-1, 9}
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