1. Solving Equations Timestamps: 43:20 · 54:33

Removing decimals — multiply by a power of 10
Example: 0.4x + 1.2 = 2 Multiply by 10 → 4x + 12 = 20 Solve → 4x = 8 → x = 2
Quadratic formula (use when ax²+bx+c=0)
x = (-b ± √(b² - 4ac)) / (2a)
Example: Solve 2x² - 4x - 6 = 0
a=2, b=-4, c=-6
x = [4 ± √(16 + 48)] / 4 = [4 ± √64] / 4 = [4 ± 8] / 4
x = 3 or x = -1

2. Factoring & Multiplying Polynomials Timestamps: 05:07 · 05:59 · 08:31

Polynomial types:
  • Monomial — single term (e.g., 5x²)
  • Binomial — two terms (e.g., x + 3)
  • Trinomial — three terms (e.g., x² + 5x + 6)
Monomial × Trinomial
3x (x² + 4x + 5) = 3x³ + 12x² + 15x
Binomial × Binomial — FOIL
(x + 3)(x + 4) ⟶ F: x·x = x² O: x·4 = 4x I: 3·x = 3x L: 3·4 = 12 Result: x² + 7x + 12

3. Properties of Exponents Timestamps: 13:16 · 14:04 · 16:15

Key rules
Multiplication: a^m · a^n = a^(m+n) e.g., x^3 · x^5 = x^8 Division: a^m / a^n = a^(m-n) e.g., x^7 / x^2 = x^5 Zero exponent: a^0 = 1 (a ≠ 0) e.g., 5^0 = 1 Negative: a^(-n) = 1 / a^n e.g., x^-3 = 1/x^3
Quick visualization: Multiplying x² by x³ is like combining two groups of powers → x^(2+3) = x^5.

4. Graphing Linear Equations Timestamps: 01:02:51 · 01:05:25

Slope-intercept form
y = mx + b m = slope (rise / run) b = y-intercept (point where line crosses the y-axis)
Given y = 2x + 1 → slope = 2, y-intercept = (0,1) Plot (0,1). From there, rise 2, run 1 to get next point (1,3).
Standard form (use intercepts)
Ax + By = C x-intercept: set y = 0 → solve for x y-intercept: set x = 0 → solve for y
2x + 3y = 6 x-intercept: y=0 → 2x=6 → x=3 → (3,0) y-intercept: x=0 → 3y=6 → y=2 → (0,2)

5. Writing the Equation of a Line Timestamps: 01:06:53 · 01:09:18 · 01:12:30

Point-Slope form
y - y₁ = m(x - x₁)
Point (2,3), m = 4: y - 3 = 4(x - 2) → y = 4x - 8 + 3 → y = 4x - 5
Two points → find slope
m = (y₂ - y₁) / (x₂ - x₁)
Points (1,2) & (3,6): m = (6 - 2) / (3 - 1) = 4/2 = 2 Use point-slope: y - 2 = 2(x - 1) → y = 2x
Parallel & perpendicular
  • Parallel lines → same slope
  • Perpendicular lines → slope is negative reciprocal (m₂ = -1/m₁)
Line parallel to y = 3x + 1 through (2,4): y - 4 = 3(x - 2) → y = 3x - 2
Line perpendicular to y = (1/2)x + 1 through (0,0): slope = -2 → y = -2x