Study sets matching "polynomials chapter 5"

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Study sets matching "polynomials chapter 5"

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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…
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…
Chapter 5 Polynomials
Monomial
Binomial
Trinomial
Polynomial
1 Term
2 Terms
3 Terms
4 Terms
Monomial
1 Term
Binomial
2 Terms
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)
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
...
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
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
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
Chapter 5: Exponents and Polynomials
Positive Integral Exponents
Negative Integral Exponents
Zero Exponent
Product Rule of Exponents
If x is a nonzero real number, and n is a positive integer, t…
If x is a nonzero real number, and n is a negative integer, t…
If a is any nonzero real number, then a⁰=1
If m and n are integers, and a=0, then aᵐ × aⁿ = aᵐ⁺ⁿ
Positive Integral Exponents
If x is a nonzero real number, and n is a positive integer, t…
Negative Integral Exponents
If x is a nonzero real number, and n is a negative integer, t…
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…
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
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…
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
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
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
Chapter 5: Polynomials
monomial
Degree of the Monomial
Rule For Multiplying Exponential Expre…
Rule For Dividing Exponential Expressi…
a number, a variable, or a product of a number and variables.
sum of the exponents of the variables
If same base and multiplying= add exponents
If same base and dividing= subtract the exponents
monomial
a number, a variable, or a product of a number and variables.
Degree of the Monomial
sum of the exponents of the variables
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
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…
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…
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
classyifying polynomials Chapter 5
0
1
2
3
constant
linear
quadratic
cubic
0
constant
1
linear
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 coeffients (not bases) and add exponents... x^m+n
multiply exponents, if there is a coefficient, multiply that…
multiply the variables by the exponent... x^m y^m
subtract the exponents... x^m-n
when multiplying two numbers with expo…
multiply coeffients (not bases) and add exponents... x^m+n
when a number with an exponent has an…
multiply exponents, if there is a coefficient, multiply that…
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.
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…
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.
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
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
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
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
12 terms
Prentice Hall Algebra 1 Chapter 5 Polynomials
Polynomial
Degree
Multiplying two binomials
Linear
An expression that has no operations other than addition, sub…
The highest power of a variable that appears in a polynomial…
1. Multiply each term of one term by the other. 2. Combine li…
A word describing a first degree polynomial
Polynomial
An expression that has no operations other than addition, sub…
Degree
The highest power of a variable that appears in a polynomial…
Chapter 5 Polynomial Functions Theorems
Remainder theorem
Factor theorem
Fundamental Theorem of Algebra
Conjugate root theorem
A theorem that states: for a polynomial P(x), the value P(c)…
A remainder theorem that states that the polynomial p(x) has…
A theorem that says every polynomial function with a degree o…
A theorem that says if a + bi is root of a polynomial with re…
Remainder theorem
A theorem that states: for a polynomial P(x), the value P(c)…
Factor theorem
A remainder theorem that states that the polynomial p(x) has…
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…
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…
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…
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)
17 terms
Unit 5 - Factoring Polynomials
Polynomial
Standard Form of a Polynomial
Coefficient
Monomial
A monomial or a sum or difference of monomials.
Arrangement of terms in a polynomial where the highest degree…
A number that is multiplied by a variable.
A number or a product of numbers and variables with whole-num…
Polynomial
A monomial or a sum or difference of monomials.
Standard Form of a Polynomial
Arrangement of terms in a polynomial where the highest degree…
Unit 5 - Factoring Polynomials
Polynomial
Standard Form of a Polynomial
Coefficient
Monomial
A monomial or a sum or difference of monomials.
Arrangement of terms in a polynomial where the highest degree…
A number that is multiplied by a variable.
A number or a product of numbers and variables with whole-num…
Polynomial
A monomial or a sum or difference of monomials.
Standard Form of a Polynomial
Arrangement of terms in a polynomial where the highest degree…
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
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+…
Keller: Algebra 2:: Chapter 5, Polynomials, Section 1 Study Guide
Define monomial
What is an example of a monomial?
What is the degree of a monomial? (in…
What is a polynomial?
a real number, variable, or product of a real number and one…
y = 16
the exponent of the variable
a monomial or sum of monomials
Define monomial
a real number, variable, or product of a real number and one…
What is an example of a monomial?
y = 16
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.
17 terms
Chapter 2 - Polynomials
Scientific Notation
polynomial
polynomial functions
leading coefficient
A number expressed in the form m × 10n
is a monomial or a sum of monomials
a polynomial is the sum of one or more monomials with real co…
The coefficient of the term with the highest degree
Scientific Notation
A number expressed in the form m × 10n
polynomial
is a monomial or a sum of monomials
Chapter 9 Polynomials
monomials
polynomials
binomial
trinomial
a number, variable, or a product of numbers and variables wit…
monomial or sum of monomials
polynomial with two terms
polynomial with three terms
monomials
a number, variable, or a product of numbers and variables wit…
polynomials
monomial or sum of monomials
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
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.
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
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…
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