What’s in Unit 5
This unit covers exponent rules, negative exponents, scientific notation, defining & classifying polynomials, multiplying (FOIL and distribution), special products, and dividing polynomials by monomials and simple binomials.
These topics map to Chapter 5 of the Beginning Algebra OER (Sections 5.1–5.7). See References for links.
5.1 Exponent Properties
- Product: aman = am+n
- Power: (am)n = amn
- Power of product: (ab)n = anbn
- Quotient: am/an = am−n, a ≠ 0
- Zero exponent: a0 = 1 (a ≠ 0)
Example
(x3y)(x2y5) = x5y6
5.2 Negative Exponents
a−n = 1/an; move across the fraction bar to make exponents positive.
Example
x−3y2 / x = y2 / x4.
5.3 Scientific Notation
c × 10n where 1 ≤ c < 10 and n ∈ ℤ. Move decimal left → n positive; right → n negative.
Example
0.00056 = 5.6 × 10−4.
5.4 Intro to Polynomials
- Monomial / binomial / trinomial
- Degree of a term & overall degree
- Standard form: descending powers
5.5 Multiply Polynomials
Example
(2x + 3)(x − 5) = 2x² − 7x − 15
5.6 Special Products
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
5.7 Divide Polynomials
Example
(6x³ − 9x²)/3x = 2x² − 3x
Audio/Class Review (optional)
Place recordings in an audio/ folder (same level as this file). If they exist, players appear below.
Recognized names: Math025*.m4a or Math 025*.m4a.