methods / polynomials.mdon commit add factorising notes for methods (90a521d)
   1# Polynomials
   2
   3## Factorising
   4
   5#### Quadratics
   6**Quadratics:** $x^2 + bx + c = (x+m)(x+n)$ where $mn=c$, $m+n=b$  
   7**Difference of squares:** $a^2 - b=^2 = (a - b)(a + b)$  
   8**Perfect squares:** $a^2 \pm 2ab + b^2 = (a \pm b^2)$  
   9**Completing the square (monic):** $x^2+bx+c=(x+{b\over2})^2+c-{b^2\over4}$  
  10**Completing the square (non-monic):** $ax^2+bx+c=a(x-{b\over2a})^2+c-{b^2\over4a}$  
  11**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$
  12
  13#### Cubics
  14**Difference of cubes:** $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$  
  15**Sum of cubes:** $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$  
  16**Perfect cubes:** $a^3 \pm 3a^2b + 3ab^2 \pm b^3 = (a \pm b)^3$