1# Polynomials
2## Factorising
4#### 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 $\Delta=b^2-4ac$ (if $\Delta$ is a perfect square, rational roots)
12#### 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:** $a^3 \pm 3a^2b + 3ab^2 \pm b^3 = (a \pm b)^3$
17## Linear and quadratic graphs
19$$y=mx+c, \quad {x \over a} + {y \over b}=1$$
21Parallel lines - $m_1 = m_2$
23Perpendicular lines - $m_1 \times m_2 = -1$