Math Review: Section 1.1 - 1.3

Natural Numbers

Counting numbers starting from 1. They do not include 0 or negatives

Whole Numbers

Natural numbers including 0

Integers

Whole numbers and their negatives

Rational Numbers

Numbers that can be written as a fraction

Irrational Numbers

Numbers that cannot be written as a simple fraction; their decimal expansions are non-repeating and non-terminating

Real Numbers

All numbers

What is needed for an equation to be considered a polynomial?

No negative exponents & all coefficients that are real numbers.

Degree

Highest exponent on a variable

Leading Coefficient

Coefficient under the degree

Always put answers that what form?

Standard form

What if there is a tie in the polynomial?

Terms are changeable & there would be more than 1 LC

Suppose there are groups of coefficients. How would I organize them?

Highest sum - lowest sum

What rules apply when combining like-terms?

Same variable & exponent

x³ x x² = ?

x5

(x²)³

x6

(u+v)(u-v)

u² - v²

(u+v)² =

(u-v)² =

u² + 2uv + v² & u² - 2uv + v²

(u+v)³ =

(u-v)³ =

u³ + 3u²v + 3uv² + v³ & u³ - 3u²v + 3uv² - v³

a + b = b + a

Addition Commutative

(a + b) + c = a + (b + c)

Addition Associative

a + 0 = a = 0 + a

Addition Identity

a + (-a) = 0 = (-a) + a

Addition Inverse

a(b + c) = ab + ac & (b + c)a = ba +ca

Distributive Addition & Multiplication

a × b = b × a

Multiplication Commutative

(ab)c = a(bc)

Multiplication Associative

a x 1 = a = 1 x a

Multiplication Identity

a x 1/a = 1 = 1/a x a. a ≠ 0

Multiplication Inverse