MATH-UA 120 Lecture Notes - Lecture 5: Imaginary Number, Imaginary Unit, Completing The Square
Document Summary
Natural (counting) numbers: positive numbers > 0 (not fractions/decimals) Rational numbers: any number that can be written as a fraction. Irrational numbers: any number that cannot be written as a fraction. Given an equation with multiple variables and we solve for one of them, we are solving a literal equation. Laws of exponents: am an = am+n. 8. orrrr (but the first one is usually easier) Multiplying polynomials: monomial x polynomial : distribute monomial to each term in the polynomial, binomial x binomial : first outside inside last. Factoring cubes: a3 + b3 = (a + b)(a2 ab + b2) : sum of two cubes, a3 - b3 = (a - b)(a2 + ab + b2) : difference of two cubes. Trinomial = (binomial)(binomial) ax2 + bx + c (quadratic) Ex: (x 4)(x + 2) = x2 2x 8. 5x (3x - 2) 2 (3x 2) (5x 2)(3x 2)
