A polynomial of degree n: f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₀, where aₙ ≠ 0.

For an ellipse: c² = a² - b², where c is the distance from center to each focus.

Common ratio r = any term divided by the previous term: r = aₙ/aₙ₋₁.

A rational function is p(x)/q(x) where p and q are polynomials and q(x) ≠ 0.

A circle has eccentricity = 0. Ellipse: 0<e1.

Quotient rule: log(a/b) = log(a) - log(b). Division inside becomes subtraction outside.

i² = -1 by definition. This is the fundamental property of the imaginary unit.

For a hyperbola: c² = a² + b². The foci are farther from the center than the vertices.

Rational Root Theorem: possible rational roots = ±(factors of constant term a₀)/(factors of leading coeff aₙ).

De Moivre's Theorem: [r(cosθ+i sinθ)]ⁿ = rⁿ(cos(nθ)+i sin(nθ)). Used to raise complex numbers to powers.

Sum of squares 1²+2²+...+n² = n(n+1)(2n+1)/6.

Scalar multiplication: multiply every element of the matrix by k. (kA)ᵢⱼ = k × Aᵢⱼ.

For parabola y = ax², the focus is at (0, 1/(4a)). The directrix is y = -1/(4a).

Geometric series sum: Sₙ = a₁(1-rⁿ)/(1-r). Use when you know first term, ratio, and number of terms.

Pascal's Triangle gives the binomial coefficients for expanding (a+b)ⁿ. Row n gives coefficients for (a+b)ⁿ.

The imaginary unit i = √(-1), so i² = -1. Complex numbers are written as a + bi.

y=0 is the horizontal asymptote when degree of numerator < degree of denominator. The fraction approaches 0.