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Study sets matching "polynomials chapter 5"

27 terms
Chapter 5 Polynomials and Polynomial Functions
monomial
degree of a monomial
polynomial
degree of a polynomial
Is a real number, a variable, or a product of a real number a…
The degree of a monomial in one variable is the exponent of t…
a monomial or a sum of monomials
The degree of a polynomial in one variable is the greatest de…
monomial
Is a real number, a variable, or a product of a real number a…
degree of a monomial
The degree of a monomial in one variable is the exponent of t…
25 terms
Chapter 5 Polynomials and Polynomial Functions
monomial
degree of a monomial
polynomial
polynomial function
Is a real number, a variable, or a product of a real number a…
The degree of a monomial in one variable is the exponent of t…
a monomial or a sum of monomials
...
monomial
Is a real number, a variable, or a product of a real number a…
degree of a monomial
The degree of a monomial in one variable is the exponent of t…
15 terms
Chapter 5 - Polynomials
monomial
binomial
trinomial
quadratic
a polynomial with one term
a polynomial with two terms
a polynomial with three terms
a polynomial of degree 2
monomial
a polynomial with one term
binomial
a polynomial with two terms
27 terms
Chapter 5 Polynomials
Monomial
Binomial
Trinomial
Polynomial
1 Term
2 Terms
3 Terms
4 Terms
Monomial
1 Term
Binomial
2 Terms
23 terms
Chapter 5: Polynomials and Polynomial Functions
Binomial Theorem
degree of a monomial
degree of a polynomial
end behavior
For every positive integer
...
...
...
Binomial Theorem
For every positive integer
degree of a monomial
...
18 terms
chapter 5 polynomials
monomial
degree of a monomial
polynomial
degree of a polynomial
A polynomial with one term
The exponent of the variable (3x^2 -> degree = 2)
A monomial or sum of monomials
The highest exponent of a variable in the polynomial
monomial
A polynomial with one term
degree of a monomial
The exponent of the variable (3x^2 -> degree = 2)
13 terms
Chapter 5 Polynomials
polynomial
polynomial function
synthetic substitution
end behavior
a monomial or a sum of monomials
a function of the form... the exponents are all whole numbers…
a method used to evaluate a polynomial function
the behavior of the graph of a function as x approaches posit…
polynomial
a monomial or a sum of monomials
polynomial function
a function of the form... the exponents are all whole numbers…
48 terms
Chapter 5 Polynomials
Products of Exponents... Product of Powers
Products of Exponents... Power of a Power
Products of Exponents... Power of a Product
Products of Exponents... Negative Exponent
a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ
(a ⁿ )ⁿ = a ⁿⁿ
(ab) ⁿ = a ⁿb ⁿ
a⁻ⁿ = 1/aⁿ , a ≠ 0
Products of Exponents... Product of Powers
a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ
Products of Exponents... Power of a Power
(a ⁿ )ⁿ = a ⁿⁿ
8 terms
Math-Chapter#5: Polynomials
(A + B)²
(A - B)²
(A + B)(A - B)
(A + B)³
= A² + 2AB + B²
= A² -2AB + B²
= A² - B²
= A³ + 3A²B + 3AB² + B³
(A + B)²
= A² + 2AB + B²
(A - B)²
= A² -2AB + B²
28 terms
Chapter 5: Polynomials & Polynomial Functions
Constant
Linear
Quadratic
Cubic
degree of 0
degree of 1
degree of 2
degree of 3
Constant
degree of 0
Linear
degree of 1
17 terms
vocab chapter 5 polynomials
degree
descending
ascending
polynomial
highest "power" of a variable
decreasing from large-small
increasing from small-large
an expression using only +, -, * of or by the variable
degree
highest "power" of a variable
descending
decreasing from large-small
15 terms
Chapter 5 - Polynomials
Rule - Zero Exponent
Example of Zero Exponent
Rule - Negative Exponent
Example of Negative Exponent
If x=/0, then x^0=1
47^0=1
If x=/0, then x^-n = 1/x^n
7^-2 = 1/7^2 = 1/49
Rule - Zero Exponent
If x=/0, then x^0=1
Example of Zero Exponent
47^0=1
10 terms
Algebra Chapter 5 - Polynomials and Polynomial Functions
Polynomial/Polynomial Function
Synthetic Substitution
End Behavior
Factor Completely
A polynomial is a monomial or a sum of monomials. A polynomia…
Another way to evaluate a polynomial function is to use synth…
The end behavior of a function's graph os the behavior of the…
A factorable polynomial with integer coefficients is factored…
Polynomial/Polynomial Function
A polynomial is a monomial or a sum of monomials. A polynomia…
Synthetic Substitution
Another way to evaluate a polynomial function is to use synth…
25 terms
SREB Vocab. - Chapter 5 (Polynomials and Polynomial Functions)
polynomial
factoring
conjugates
SOPPS
a finite sum of terms in which all variables are raised to wh…
writing a polynomial as a product
(a - b) and (a + b)... only the second sign is opposite
acronym for factoring sum/diff of cubes... *S*quare... *O*pposite *…
polynomial
a finite sum of terms in which all variables are raised to wh…
factoring
writing a polynomial as a product
10 terms
Vocabulary for Polynomials, Chapter 5
End behavior
Local Maximum
Local Minimum
Zeros
Describes the direction of the y-values as x goes to positive…
A peak in the y-values of the graph of the function, but not…
A low in the y-values of the graph of the function, but not t…
Where the graph of the function touches or crosses the y-axis.
End behavior
Describes the direction of the y-values as x goes to positive…
Local Maximum
A peak in the y-values of the graph of the function, but not…
16 terms
Math Chapter 5: Polynomials
monomial
binomial
trinomial
polynomial
1 term
2 terms
3 terms
an algebraic expression made up of terms connected by the ope…
monomial
1 term
binomial
2 terms
19 terms
Chapter 5- Polynomials Quest
What is the product of a power?
What is the power of a power?
What is the power of a product?
What is scientific notation?
a^m*a^n=a^m+n
(a^m)^n=a^mn
(ab)^m=a^m*b^m
ax10^h
What is the product of a power?
a^m*a^n=a^m+n
What is the power of a power?
(a^m)^n=a^mn
10 terms
Chapter 5 Vocabulary (Polynomials and Polynomial Functions)
end behavior
monomial
multiplicity
Pascal's Triangle
describes the directions of the graph as you move to the left…
either a real number, a variable, or the product of real numb…
the number of times the related linear factor is repeated in…
a triangular array of numbers in which the first and last num…
end behavior
describes the directions of the graph as you move to the left…
monomial
either a real number, a variable, or the product of real numb…
5 terms
classyifying polynomials Chapter 5
0
1
2
3
constant
linear
quadratic
cubic
0
constant
1
linear
13 terms
chapter 5 Polynomials and monomials
polynomial
monomials
1 term
2 terms
A sum and or difference of one or more monomial.
a term made of the product of one or more contants and/or var…
monomial ex: 3x
binomial ex: 5x(2)=7
polynomial
A sum and or difference of one or more monomial.
monomials
a term made of the product of one or more contants and/or var…
46 terms
Alg. II: Chapter 5 (Polynomials)
when multiplying two numbers with expo…
when a number with an exponent has an…
when two variables are being multiplie…
when the same variable with different…
multiply numbers and add exponents... x^m+n
multiply exponents... x^mn
multiply the variables by the exponent... x^m y^m
subtract the exponents... x^m-n
when multiplying two numbers with expo…
multiply numbers and add exponents... x^m+n
when a number with an exponent has an…
multiply exponents... x^mn
20 terms
Algebra 2 Pearson - Chapter 5 Vocabulary Polynomials
monomial
binomial
trinomial
polynomial
Any numeral, variable, or a product of a numeral and one or m…
A polynomial with two terms.
A polynomial with three terms.
A monomial or sum of terms that are monomials.
monomial
Any numeral, variable, or a product of a numeral and one or m…
binomial
A polynomial with two terms.
18 terms
Unit 5: Polynomials & Polynomial Functions
Binomial Theorem
Conjugates
Degree of a Polynomial
Difference of Cubes
Binomials of the form a + √b and a - √b.
The greatest of the degrees of its terms after it has been si…
Binomial Theorem
Conjugates
Binomials of the form a + √b and a - √b.
17 terms
Head's Vocabulary [CHAPTER 5: POLYNOMIALS AND POLYNOMIAL FUNCTIONS]
degree of a polynomial
depressed polynomial
end behavior
extrema
The degree of the monomial with the greatest degree
A polynomial that has a degree one less than the original pol…
The behavior of the graph of f(x) as x approaches positive in…
The maximum and minimum values of a polynomial function
degree of a polynomial
The degree of the monomial with the greatest degree
depressed polynomial
A polynomial that has a degree one less than the original pol…
21 terms
Honors Algebra 2: Chapter 5 Polynomials and Polynomial Functions
Monomial
Degree of a Monomial
Degree of a Polynomial
Standard Form of a Polynomial Function
a real number, a variable, or a product of real numbers and v…
the exponent of a variable
the greatest degree among its monomial terms
terms are listed in descending order of degree, and like term…
Monomial
a real number, a variable, or a product of real numbers and v…
Degree of a Monomial
the exponent of a variable
14 terms
Algebra 2 Homors Chapter 5 Polynomials
Degree of a Polynomial
Depressed Polynomial
End Behavior
Extrema
The highest degree in a polynomials
The result of dividing polynomials
What direction the graph is going
A maximum or minimum
Degree of a Polynomial
The highest degree in a polynomials
Depressed Polynomial
The result of dividing polynomials
30 terms
Algebra 2 Chapter 5: Roots of Polynomials
x^2 + 1 = 0
i
i^0
i^1
No real solutions
√-1
1
i
x^2 + 1 = 0
No real solutions
i
√-1
15 terms
Chapter 9: Polynomials
Monomial
Binomial
Trinomial
Degree of a Monomial
a polynomial with one term
a polynomial with two terms
a polynomial with three terms
the sum of the exponents of the variables in a monomial
Monomial
a polynomial with one term
Binomial
a polynomial with two terms
11 terms
Chapter 8 - Polynomials
Monomial
Binomial
Trinomial
Polynomial
a real number, variable or the product of a real number and a…
Two monomials added or subtracted
Three monomials added or subtracted
Four or more monomials added or subtracted
Monomial
a real number, variable or the product of a real number and a…
Binomial
Two monomials added or subtracted
15 terms
Chapter 6 - Polynomials
Monomial
Degree of a monomial
Polynomial
Degree of a polynomial
A number, a variable, or a product of numbers and variables w…
The sum of the exponents of the variables.
A monomial or a sum or difference of monomials.
The degree of the term with the greatest degree.
Monomial
A number, a variable, or a product of numbers and variables w…
Degree of a monomial
The sum of the exponents of the variables.
6 terms
Algebra 1 Ch 5: Polynomials and polynomial functions
polynomial
degree
like terms
GCF
one or more terms
______ of a monomial --> If a ≠ 0, the degree of axn is n. Th…
Terms that have the same variables AND the same... exponents.
greatest common factor
polynomial
one or more terms
degree
______ of a monomial --> If a ≠ 0, the degree of axn is n. Th…
20 terms
Polynomials (Ch 5) and Equations (Ch 2) - Terms
binomial
highest
coefficient
trinomial
A polynomial containing two terms is called a ________.
The degree of a polynomial is the degree of its ___________ d…
The numerical factor in a monomial is called the __________.
A polynomial containing three terms is called a __________.
binomial
A polynomial containing two terms is called a ________.
highest
The degree of a polynomial is the degree of its ___________ d…
6 terms
Chapter 5.4 Multiplying Polynomials (note: goal is to perform most task mentally)
Multiplying Monomials
Multiplying Monomials With More Than O…
Multiplying a Monomial by a Polynomial
Multiplying Two Polynomials
First we multiply the coefficients, and then we multiply the…
First we multiply the coefficients, and then we multiply the…
We multiply the monomial by each term of the polynomial.... To d…
To multiply Polynomials containing more than two terms, we mu…
Multiplying Monomials
First we multiply the coefficients, and then we multiply the…
Multiplying Monomials With More Than O…
First we multiply the coefficients, and then we multiply the…
25 terms
Algebra 2 Chapter 5- Polynomial Functions
monomial
binomial
trinomial
polynomial
a real number, variable or product of a real number and one o…
two monomials connected with addition or subtraction... ex. 3x²+…
three monomials connected with addition or subtraction... ex. x⁴…
a monomial or a sum of monomials
monomial
a real number, variable or product of a real number and one o…
binomial
two monomials connected with addition or subtraction... ex. 3x²+…
14 terms
Alg 34 Ch 5 Polynomials: Degree, Zeros, & Multiplicity
What is the degree of y = -2x+5 ?
What is the degree of f(x)=x^4 + 2x^3 ?
What is the degree of y= (x+1)(x-4)(x+…
What is the degree of y = [ (x+5)^2][(…
1
4
3
11
What is the degree of y = -2x+5 ?
1
What is the degree of f(x)=x^4 + 2x^3 ?
4
9 terms
MA-380 Chapter 5: Polynomial Functions
Sum and Difference: (a + b)(a - b)
Square of a Binomial: ... (a + b)^2... (a -…
Sum of Two Cubes: a^3 + b^3
Cube of a Binomial:... (a + b)^3... (a - b)^3
a^2 - b^2
a^2 + 2ab + b^2 ... a^2 - 2ab + b^2
(a + b)(a^2 - ab + b^2)
a^3 + 3a^2b + 3ab^2 + b^3... a^3 - 3a^2b + 3ab^2 - b^3
Sum and Difference: (a + b)(a - b)
a^2 - b^2
Square of a Binomial: ... (a + b)^2... (a -…
a^2 + 2ab + b^2 ... a^2 - 2ab + b^2
25 terms
Unit 5 Polynomials #3b (challenging) - Multiplying Polynomials
u(30u-2)(30u+2)
x²(x-5)(x+5)
(3m+1)(2m+5)
(1-4w)(3-2w)
900u³-4u
x⁴-10x³+25x²
6m²+17m+5
3-14w+8w²
u(30u-2)(30u+2)
900u³-4u
x²(x-5)(x+5)
x⁴-10x³+25x²
13 terms
Unit 5 Polynomials #3b (challenging) - Multiplying Polynomials
900x³ - 4x
x⁴ - 10x³ + 25x²
6x² + 17x + 5
8x² - 14x + 3
Multiply... x(30x - 2)(30x + 2)
Multiply... x²(x - 5)(x + 5)
Multiply... (3x + 1)(2x + 5)
Multiply... (1 - 4x)(3 - 2x)
900x³ - 4x
Multiply... x(30x - 2)(30x + 2)
x⁴ - 10x³ + 25x²
Multiply... x²(x - 5)(x + 5)
10 terms
Chapter 8 Polynomials and Factoring
binomial
degree of a monomial
degree of a polynomial
difference of two squares
a polynomial consisting of two terms or monomials.
is the sum of exponents of its variables.
is the same as the degree of the monomial with the greatest d…
The difference pf two perfect square monomials.
binomial
a polynomial consisting of two terms or monomials.
degree of a monomial
is the sum of exponents of its variables.
14 terms
Unit 5 "Polynomials" Vocabularies
Polynomial
Monomial
Binomial
Trinomial
one term or the sum/difference of terms whose variables have…
a polynomial with only one term 单项式
a polynomial with two terms 二项式
a polynomial with three terms 三项式
Polynomial
one term or the sum/difference of terms whose variables have…
Monomial
a polynomial with only one term 单项式
9 terms
Grade 9 Math (Math Links) Chapter 5 Introduction to Polynomials
Algebra
Term
Polynomial
Monomial
a branch of mathematics that uses symbols to represent unknow…
an expression formed from the product of numbers and or varia…
an algebraic expression made up of terms connected by the ope…
an algebraic expression with ONE term. 6y
Algebra
a branch of mathematics that uses symbols to represent unknow…
Term
an expression formed from the product of numbers and or varia…
21 terms
Unit 5 - Polynomials
Polynomial function
Degree
Leading term
Leading coefficient
A function with any number of terms where each term is in the…
Value of a term's exponent
Term with highest degree
Largest number in front of a variable
Polynomial function
A function with any number of terms where each term is in the…
Degree
Value of a term's exponent
17 terms
Chapter 3 - Polynomials
monomial
polynomial
degree of a monomial
degree of a polynomial
a number or a product of numbers and variables with whole num…
a monomial or a sum or difference of monomials
the sum of the exponents of the variables
given by the term with the greatest degree
monomial
a number or a product of numbers and variables with whole num…
polynomial
a monomial or a sum or difference of monomials
23 terms
Chapter 6 polynomials
Constant
Linear
Quadratic
Cubic
A Degree of 0
A Degree of 1
A Degree of 2
A Degree of 3
Constant
A Degree of 0
Linear
A Degree of 1
17 terms
Chapter 3 - Polynomials
monomial
polynomial
degree of a monomial
degree of a polynomial
a number or a product of numbers and variables with whole num…
a monomial or a sum or difference of monomials
the sum of the exponents of the variables
given by the term with the greatest degree
monomial
a number or a product of numbers and variables with whole num…
polynomial
a monomial or a sum or difference of monomials
13 terms
Unit 5 Polynomials #1 - Vocabulary
Monomial
Constant
Coefficient
Degree
A polynomial with one term.
is a monomial containing no variables.
is a number in front of the variable.
is the exponent of the variable.
Monomial
A polynomial with one term.
Constant
is a monomial containing no variables.
15 terms
Unit 5: Polynomials & Factoring (Chapters 7 & 8)
Monomial
Polynomial
Degree of a Monomial
Constant Term
a number, a variable, or the product of a number, and one or…
a monomial or a sum or difference of two or more monomials.
the sum of the exponents of the variables in the monomial.
a term that has no variable part is called a constant term, o…
Monomial
a number, a variable, or the product of a number, and one or…
Polynomial
a monomial or a sum or difference of two or more monomials.
28 terms
Chapter 6: Polynomials and Polynomial Functions
simplify
degree of polynomial
synthetic divison
polynomial in one variable
rewriting an expression without parenthesis or negative expon…
degree of the monomial with the highest degree
a simpler process of dividing a polynomial by a binomial
only "x"
simplify
rewriting an expression without parenthesis or negative expon…
degree of polynomial
degree of the monomial with the highest degree
14 terms
Unit5 Polynomials Vocabulary Words
Polynomial
Monomial
Binomial
Trinomial
a mathematical function that is a number of terms (多项式)
a polynomial which only has one term (单项式)
a polynomial which has two terms (二项式)
a polynomial which has three terms (三项式)
Polynomial
a mathematical function that is a number of terms (多项式)
Monomial
a polynomial which only has one term (单项式)
21 terms
Chapter 9: Polynomials and Factoring
monomial
degree of a monomial
polynomial
degree of a polynomial
a number, variable, or the product of a number and one or mor…
the sum of the exponents of the variables in the monomial
a monomial or a sum of monomials, each called a term of the ___
the greatest degree of all the terms
monomial
a number, variable, or the product of a number and one or mor…
degree of a monomial
the sum of the exponents of the variables in the monomial
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