From 90a521de14e102aad1674b4e9b60e41062372504 Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sun, 2 Dec 2018 14:27:44 +1100
Subject: [PATCH] add factorising notes for methods

---
 methods/polynomials.md | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)
 create mode 100644 methods/polynomials.md

diff --git a/methods/polynomials.md b/methods/polynomials.md
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+# Polynomials
+
+## Factorising
+
+#### Quadratics
+**Quadratics:** $x^2 + bx + c = (x+m)(x+n)$ where $mn=c$, $m+n=b$  
+**Difference of squares:** $a^2 - b=^2 = (a - b)(a + b)$  
+**Perfect squares:** $a^2 \pm 2ab + b^2 = (a \pm b^2)$  
+**Completing the square (monic):** $x^2+bx+c=(x+{b\over2})^2+c-{b^2\over4}$  
+**Completing the square (non-monic):** $ax^2+bx+c=a(x-{b\over2a})^2+c-{b^2\over4a}$  
+**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$
+
+#### Cubics
+**Difference of cubes:** $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$  
+**Sum of cubes:** $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$  
+**Perfect cubes:** $a^3 \pm 3a^2b + 3ab^2 \pm b^3 = (a \pm b)^3$  
-- 
2.47.1