Factorizing & Quadratics

Difference of Squares

a² - b² = (a + b)(a - b)

Quadratic Equation

Determining the Nature of Roots of a Quadratic Equation

We do this based off the discriminant (b² - 4ac)

b² - 4ac > 0 has two real, distinct roots

b² - 4ac = 0 has real, equal roots
b² - 4ac < 0 has no real roots

Roots of Quadratic

Making Quadratic with New Roots

Manipulating the Roots of a Quadratic

Equations Reducible to a Quadratic
(Examples)

2^2x+1 —> (2^x)² × 2¹

x + √x —> √x = y
x = y²

x⁴ + x² —> x² = y
x⁴ = y²