Factoring a cubic inequality

Proved

WorkbookSource.problem_44189

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

So we need to prove that: $p^3-8p^2+15p \le 0 \Leftrightarrow p(p-3)(p-5) \le 0$

Source: InternLM Lean-Workbook, record lean_workbook_44189; Apache-2.0. Complete source proposition preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_44189 (p : ℝ) : p^3 - 8 * p^2 + 15 * p ≤ 0 ↔ p * (p - 3) * (p - 5) ≤ 0  :=  by sorry

Source