Home
Subjects
Explanations
Create
Study sets, textbooks, questions
Log in
Sign up
Upgrade to remove ads
Only $35.99/year
Math Study Guide
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
Terms in this set (39)
(True or false.) There are more than 1 type of polynomials.
True, there are monomials, binomials, trinomials, and polynomials.
(Fill in the blank) A monomial has __ number of terms
1
(Fill in the blank) a binomial has __ number of terms
2
(Fill in the blank) a trinomial has __ number of terms
3
(Fill in the blank) a polynomial has __ number of terms
1 or more
(Define) degree of a monomial
is the sum of the exponents of the variables
(Define) degree of a polynomial
the degree of the monomial term with the highest degree
(Fill in the blank) Writing polynomials in standard for is when you write the monomial terms in __________ _______ order.
descending degree
(Define) leading term
a polynomial is the term with the highest degree
(define.) leading coefficient
the coefficient of the leading term.
(Example) Associative Property
(a + b) + c = a + (b + c)
and
(ab)c = a(bc)
(Example) Commutative Property
a + b = b + a
and
ab = ba
(Example) Identity Property
a + 0 = a = 0 + a
and
a ∙ 1 = a = 1 ∙ a
(Example) Inverse Property
a + (−a) = 0 = (−a) + a
and
a∙ 1/a = 1 = 1/a (if a doesn't equal 0.)
(Example) Distributive Property
a(b + c) = ab + ac
and
ab + ac = a(b + c)
(Example) Multiplicative
Property of Zero
a ∙ 0 = 0 = 0 ∙ a
(Example) Zero Product
If ab = 0, then a = 0 or b = 0.
(Example) Reflexive
Property
a = a
(Example) Symmetric
Property
If a = b, then b = a.
(Example) Transitive
Property
If a = b and b = c, then a = c.
and
If a > b and b > c, then a > c.
(Example) Addition
Property
If a = b, then a + c = b + c
and
If a < b, then a + c < b + c.
(Example) Subtraction
Property
If a = b, then a ‐ c = b ‐ c
and
If a < b, then a ‐ c < b ‐ c.
(Example) Multiplication
Property
If a = b, then ac = bc.
and
If a < b and c > 0, then ac < bc.
(Example) Division
Property
if a = b and c does not equal 0, then a/c = b/c
and
if a<b and c>0, then a-c < b/c
(Example) Substitution
Property
If a = b, then b can be substituted for a in any equation or inequality.
(Fill in the blank) The order of the numbers can be ____ without affecting the _____ or _____. (When talking about commutative property.)
changed
sum
product
(Fill in the blank) If (a) and (b) are real numbers, then (a)+(b)=_____ and/or (a)∙(b)=______. (When talking about commutative property.)
(b)+(a)
(b)∙(a)
(Fill in the blank) The ____ of the numbers does not change. (When talking about associative property.)
order
(Fill in the blank) The grouping of the numbers can change and doesn't affect the _______ or _______. (When talking about associative property.)
sum
product
(Fill in the blank) If (a), (b) and (c) are real numbers, then (a+b)+c= _____ and/or (ab)c= ____. (When talking about associative property.)
a+(b+c)
a∙(bc)
With properties, look closely at each piece of the problem. Should you do this?
yes, because the changes can be subtle.
What is the zero exponent property?
Anything to the power of zero equal 1.
What is the negative exponent property? Give an example.
to make it positive, you would have to put it under one. (a^-n=1/a^n)
If you have a fraction with a negative exponent in the denominator, how do you make it positive? Give an example.
you would switch the denominator up to the numerator (1/a^-n=a^n)
(The following is only true if the base is the same.) If you have a^m multiplied by a^n, how could you write this in a different way so that it would be easier to solve? What property would this be?
a^m+n
product property
(The following is only true if the base is the same.) If you have a^m divided by a^n, how could you write this in a different way so that it would be easier to solve? What property would this be?
a^m-n
quotient property
What is an example of the power of power property?
(a^m)^n=a^m∙n
What is an example of the power of a product property?
(ab)^n= a^n∙b^n
What is an example of the power of a quotient property?
(a/b)^n=a^n/b^n
Sets with similar terms
Properties of Real Numbers
24 terms
Math Properties
10 terms
Math Properties
10 terms
Algebraic Properties
33 terms
Other sets by this creator
Hosa Bowl Parliamentary Procedure
24 terms
APUSH Chapter 14 ID Terms
19 terms
quiz#2 ap lang
33 terms
Sadlier Vocabulary Unit 5
20 terms