Factoring a quadratic over the reals

Proved

WorkbookSource.problem_140

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

lean-workbooksource-checked

Factor the expression $x^2 + 4x - 1$ .

Source: InternLM Lean-Workbook, record lean_workbook_140 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_140 (x : ℝ) : x^2 + 4*x - 1 = (x + 2 + Real.sqrt 5) * (x + 2 - Real.sqrt 5)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_140; Apache-2.0

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