Unit 1: Algebra II
4x2−y+0z4
binomial
A ___ is a polynomial with three terms.
trinomial
The ___ Identify Element defines 0 as such that a+0=0+a=aa+0=0+a=a for all real numbers.
additive
The __ Property of Addition states that for any a, b,a, b, and c,a+(b+c)=(a+b)+c.c,a+(b+c)=(a+b)+c.
associative
The ___ Property of Multiplication states that for any numbers a,b,a,b, and c,a⋅(b⋅c)=(a⋅b)⋅c.c,a⋅(b⋅c)=(a⋅b)⋅c.
associative
A ___ is as polynomial with two terms.
binomial
____ is the property of an operation and a set that the performance of the operation on members of the set always yields a member of the set.
closure
The ___ Property of Addition states that for any numbers aa and b,a+b=b+ab,a+b=b+a .
commutative
The ___ Property of Multiplication states that for any numbers aa and b,a⋅b=b⋅a.b,a⋅b=b⋅a.
commutative
The ___ Property of Multiplication over Addition states that for any numbers a,b,a,b, and c,a⋅(b+c)=(a⋅b)+(a⋅c).c,a⋅(b+c)=(a⋅b)+(a⋅c).
distributive
The set of first coordinates of each ordered pair in a relation is the ___.
domain
A relation in which each domain element is paired with exactly one range element is a ___.
function
{(4,5),(5,7),(6,9),(7,0)}
function relation
_____ are numbers {0,+1,−1,+2,−2,...}{0,+1,-1,+2,-2,...}ℤ .
integers
{−2,−1,0,1,2}
integers
An ___ is a relation found by interchanging the domain and range values in each ordered pair of a relation.
inverse
The Additive ___ Property states that for every number a,a, there is a number −a,-a, such that a+(−a)=(−a)+a=0.a+(-a)=(-a)+a=0.
inverse
π : rational or irrational
irrational
√2 : rational or irrational
irrational
____ are real numbers which cannot be written as the ratio of two integers; designed withℚ_
irrational numbers
A ___ is a polynomial with one term.
monomial
x3y2zx3y2z
monomial
The ___ Identity Property defines 1 as the multiplicative identity element because for every number a,a⋅1=1⋅a=a.a,a⋅1=1⋅a=a.
multiplicative
The ___ Inverse Property states that for every number aa except 0, there is a number a−1=1aa-1=1a such that a⋅(a−1)=(a−1)⋅a=1.a⋅(a-1)=(a-1)⋅a=1.
multiplicative
It is closed under addition and multiplication but not closed under subtraction or division.
natural numbers
____ are numbers {1,2,3,4...}{1,2,3,4...} and designed with ℕ .
natural numbers
{4,5,6,7}
natural numbers whole numbers integers
A ___ is a mathematical expression consisting of constants and variables, combined with the operations of addition and multiplication.
polynomial
The ___ is the set of second coordinates of each ordered pair in a relation.
range
0.333... : rational or irrational
rational
5 : rational or irrational
rational
_____ are numbers of the form {ab∣a,b∈Z,b≠0}{ab∣a,b∈ℤ,b≠0} and designated with ℚ .
rational numbers
It is closed under addition and subtraction, multiplication and division, with the exception of division by 0 which is not defined.
rational numbers real numbers
_____ are the rational numbers together with the irrational numbers; designed with
real numbers
The ___ Property of Equality states that for any number a,a=a.a,a=a.
reflexive
A ___ is any set of ordered pairs.
relation
{(0,2),(1,3),(0,−2),(2,4)} (could be more than one)
relation
{(−1,2),(−2,1),(−3,0),(−4,−1)}
relation function
The ___ Property of Equality states that for any numbers aa and b,b, if a=b,a=b, then b=a.b=a.
symmetric
Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?"
transitive
The ___ Property of Equality states that for any numbers a,b,a,b, and c,c, if a=ba=b and b=c,b=c, then a=c.a=c.
transitive
The ___ Property states that for any numbers aa and b,b, either a<b,a<b,a=b,a=b, or a>b.a>b.
trichotomy
ax−by+4z
trinomial
Numbers {0,1,2,3,4...}{0,1,2,3,4...} are called __.
whole numbers
{0,8,9,10}
whole numbers integers
{0,5,10,15}
whole numbers intergers
