Factor Theorem & Key Identities
If $p(a) = 0$, then $(x - a)$ is a factor of polynomial $p(x)$.
Algebraic Identities:
- $(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx$
- $(x + y)^3 = x^3 + y^3 + 3xy(x + y)$
- $x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$
- If $x + y + z = 0$, then $x^3 + y^3 + z^3 = 3xyz$.
