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Study sets matching "algebra polynomials functions"

24 terms
Algebra 2 Polynomials and Polynomial Functions
Monomial in Simplified Form has:
Degree of a Polynomial
Dividend
Divisor
No powers of powers... Each base appears exactly once... All fracti…
Highest exponent in the Polynomial
Number inside the division symbol. The divisor goes into it.
Number on left of the division symbol. It goes into the divid…
Monomial in Simplified Form has:
No powers of powers... Each base appears exactly once... All fracti…
Degree of a Polynomial
Highest exponent in the Polynomial
24 terms
Algebra 2 - 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+…
24 terms
Algebra 2 - 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+…
13 terms
Polynomial Functions (Algebra 1)
Polynomial
Term (math)
Monomial
Binomial
A mathematical expression that is the sum of a number of terms.
Any coefficient and variable or constant in a mathematical ex…
A mathematical expression consisting of a single term.
A mathematical expression consisting of two terms.
Polynomial
A mathematical expression that is the sum of a number of terms.
Term (math)
Any coefficient and variable or constant in a mathematical ex…
24 terms
Algebra 2 - 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+…
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…
Algebra 2 - 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+…
10 terms
Algebra II- Polynomials and Functions
Define Coefficient
Define Term
Define Degree of a Term
Define Degree of a Polynomial
the number in a monomial, binomial or trinomial
a single number or a variable, or numbers and variables multi…
the sum of the exponents of the variables in a term.
highest degree of the term(s)
Define Coefficient
the number in a monomial, binomial or trinomial
Define Term
a single number or a variable, or numbers and variables multi…
8 terms
Algebra Polynomial Functions
odd, positive
odd, negative
even, positive
even, negative
odd, positive
odd, negative
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…
10 terms
Algebra 2 - 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+…
21 terms
Algebra 2 Polynomial Functions
restrictions of polynomials
when rewriting polynomials, put them f…
name of degree 0
name of degree 1
no negative or fraction exponents; variables cannot be in the…
high to low
constant
linear
restrictions of polynomials
no negative or fraction exponents; variables cannot be in the…
when rewriting polynomials, put them f…
high to low
24 terms
Algebra 2 - 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+…
13 terms
algebra 2 polynomial functions
standard form
degree
coefficient
degree 2
combine like terms and order from highest to loweest exponent
the highest exponent
a number in front of a variable
quadratic
standard form
combine like terms and order from highest to loweest exponent
degree
the highest exponent
16 terms
Algebra polynomial functions
Multiplicity is even
Multiplycity is odd
Multiplicity = the
Even function
Touch
Cross
Highest power
Symmetry respect to y- axis
Multiplicity is even
Touch
Multiplycity is odd
Cross
25 terms
Algebra_2A_U6_Polynomials_and_Polynomial_Functions
Binomial Theorem
Conjugate Root Theorem
constant of proportionality
degree of a monomial (in one variable)
(a + b)n = P0an + P1a(n - 1)b + P2a(n - 2)b2 + . . . + P(n n-…
The irrational roots of P(x) = 0 are conjugate pairs if P(x)…
the value of a in a power function in the form y = ax to the…
the exponent in the variable power
Binomial Theorem
(a + b)n = P0an + P1a(n - 1)b + P2a(n - 2)b2 + . . . + P(n n-…
Conjugate Root Theorem
The irrational roots of P(x) = 0 are conjugate pairs if P(x)…
25 terms
Algebra 2 - 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+…
8 terms
Algebra 2 polynomial functions
Polynomial
Polynomial function
End behavior
Factor by grouping
A monomial or a sum of monomials, each of which is called a t…
A function. Exponents are all whole numbers and coefficients…
Behavior of graph as x approaches positive infinity or negati…
Factor a polynomial with four terms.
Polynomial
A monomial or a sum of monomials, each of which is called a t…
Polynomial function
A function. Exponents are all whole numbers and coefficients…
8 terms
Algebra 2 Vocab: Polynomial Functions
Polynomial
Polynomial Function
End Behavior
Factor by Grouping
A monomial or a sum of monomials
A function of the form f(x)... the exponents are all whole nu…
The behavior of the graph of a function as x approaches posit…
To factor a polynomial with four terms by grouping, factor co…
Polynomial
A monomial or a sum of monomials
Polynomial Function
A function of the form f(x)... the exponents are all whole nu…
10 terms
Advanced Algebra: Polynomial & Function Operations
Coefficient
Degree
Binomial
Trinomial
a number multiplied by a variable
the greatest exponent of its variable
an algebraic expression of the sum or the difference of two t…
an algebraic expression of the sum or the difference of three…
Coefficient
a number multiplied by a variable
Degree
the greatest exponent of its variable
6 terms
Algebra II Polynomial Function Graphs
y=x²
y=-x²
y=x³
y=-x³
opposite of this (flipped over x axis)
y=x²
y=-x²
10 terms
Algebra 2 Polynomial Functions Names
Name Using Degree-0/ Number of Terms
Name Using Degree-1/ Number of Terms
Name Using Degree-2/ Number of Terms
Name Using Degree-3/ Number of Terms
Constant
Linear/ Monomial
Quadratic/ Binomial
Cubic/ Trinomial
Name Using Degree-0/ Number of Terms
Constant
Name Using Degree-1/ Number of Terms
Linear/ Monomial
112 terms
Algebra II - Factoring polynomials & Quadratic Functions
2, 6
1
2a
4
Identify the factors
GCF, is the highest number that divides exactly into two or m…
GCF, is the highest number that multiplies by two or more num…
If there are no common prime factors, the GCF is 1*(true = 4…
2, 6
Identify the factors
1
GCF, is the highest number that divides exactly into two or m…
12 terms
Algebra Vocabulary Unit 7 and 8 Polynomials and Polynomial Functions
Constant Term
End Behavior
Factored Completely
leading coefficient
The constant term is an expression of equation has a fixed va…
End behavior of a polynomial graph is the behavior of the gra…
A factored polynomial with integer coeffecients is factored c…
The number in front of the variable with the largest exponent
Constant Term
The constant term is an expression of equation has a fixed va…
End Behavior
End behavior of a polynomial graph is the behavior of the gra…
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+…
13 terms
Algebra Polynomials
Polynomials
Degree
Constant
Linear
named according to degree and number of terms
greatest exponent of the polynomial
degree of 0
degree of 1
Polynomials
named according to degree and number of terms
Degree
greatest exponent of the polynomial
16 terms
Algebra 2 - Chap 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+…
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
8 terms
Finding the Zeros of a Polynomial Function Algebraically
1/2, 5
−5/2, 3, 4
1/2, 1, −1
0, 1, 1
Find the zeros of f(x) = (2x − 1)(x − 5)
Find the zeros of f(x) = (2x + 5)(x² − 7x + 12)
Find the zeros of f(x) = 2x³ − x² − 2x + 1
Find the zeros of f(x) = x³ − 2x² + x
1/2, 5
Find the zeros of f(x) = (2x − 1)(x − 5)
−5/2, 3, 4
Find the zeros of f(x) = (2x + 5)(x² − 7x + 12)
14 terms
College Algebra Chapter 2: Polynomial and Rational Functions
standard form
general form
vertex
intermediate value theorem
f(x) = a(x-h)^2+k
f(x) = ax^2+bx+c
(-b/2a,f(-b/2a))
let a and b be real numbers such that a<b. If f is a polynomi…
standard form
f(x) = a(x-h)^2+k
general form
f(x) = ax^2+bx+c
12 terms
Finding the Zeros of a Polynomial Function Algebraically
1/2, 5
−5/2, 3, 4
0, 1/2, 1, −1
0, 1 mult. 2
Find the zeros of f(x) = (2x − 1)(x − 5)
Find the zeros of f(x) = (2x + 5)(x^2 − 7x + 12)
Find the zeros of f(x) = x(2x − 1)(x − 1)(x + 1)
Find the zeros of f(x) = x^3 − 2x^2 + x
1/2, 5
Find the zeros of f(x) = (2x − 1)(x − 5)
−5/2, 3, 4
Find the zeros of f(x) = (2x + 5)(x^2 − 7x + 12)
12 terms
Finding the Zeros of a Polynomial Function Algebraically
.5, 5
−2.5, 3, 4
0, .5, 1, −1
0, 1
Find the zeros of f(x) = 2x² - 11x + 5
Find the zeros of f(x) = 2x³ - 9x² - 11x + 60
Find the zeros of f(x) = 2x⁴ - x³ - 2x² + x
Find the zeros of f(x) = x³ - 2x² +x
.5, 5
Find the zeros of f(x) = 2x² - 11x + 5
−2.5, 3, 4
Find the zeros of f(x) = 2x³ - 9x² - 11x + 60
24 terms
algebra: polynomials
monomial
binomial
trinomial
polynomial
1 term
2 terms
3 terms
more than one term
monomial
1 term
binomial
2 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.
22 terms
Algebra 2: Graphing Polynomials
y = x³
y = −x³
y = x³ + 2
y = x³ + 2x² −x −2
y = x³
y = −x³
18 terms
Algebra 2 - Unit 6) Polynomial Functions
monomial
polynomial
degree of a monomial
degree of a polynomial
a number or product of numbers and variables with whole numbe…
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 product of numbers and variables with whole numbe…
polynomial
a monomial or a sum or difference of monomials
Algebra II/Trig Honors: Polynomial Functions
Standard Form
Polynomial
What is a polynomial function?
Degree of a polynomial
When the terms of a polynomial are arranged from the largest…
Expression consisting of variables and coefficients, that i…
The sum or difference of one or more monomials (a number, or…
The value of the highest exponent
Standard Form
When the terms of a polynomial are arranged from the largest…
Polynomial
Expression consisting of variables and coefficients, that i…
13 terms
(Algebra) Polynomials
Monomial
Degree of a Monomial
Polynomial
Degree of a Polynomial
a number, variable or the product of a number and one more va…
the sum of the exponents of the variables in the monomial... 3a…
a monomial or sum of monomials -- each called a term or the p…
the greatest degree in its term... 3ab² + b = Degree: 3
Monomial
a number, variable or the product of a number and one more va…
Degree of a Monomial
the sum of the exponents of the variables in the monomial... 3a…
10 terms
Algebra II : Polynomial function degree names
0
1
2
3
constant
Linear
quadratic
cubic
0
constant
1
Linear
15 terms
Polynomial Functions
Polynomial
Term (math)
Monomial
Binomial
A mathematical expression that is the sum of a number of terms.
Any coefficient and variable or constant in a mathematical ex…
A mathematical expression consisting of a single term.
A mathematical expression consisting of two terms.
Polynomial
A mathematical expression that is the sum of a number of terms.
Term (math)
Any coefficient and variable or constant in a mathematical ex…
Algebra: polynomials
term
standard form
coefficient
greatest common factor (GCF)
a single number or variable
a way of writing down very large or very small numbers easily
a numerical or constant quantity placed before and multiplyin…
the greatest factor that divides two numbers
term
a single number or variable
standard form
a way of writing down very large or very small numbers easily
35 terms
Algebra 1: EOC Polynomials
Algebraic expression
Binomial
Coefficient
Common difference
contains numbers, variables, and operations (no equal sign)
an expression that contains two terms
the "big" number in front of the variable
the constant difference between consecutive terms in a sequence
Algebraic expression
contains numbers, variables, and operations (no equal sign)
Binomial
an expression that contains two terms
20 terms
Polynomial Functions
Odd degree, Positive coeff.
Odd degree, Negative coeff.
Even degree, Positive Coeff.
Even degree, Negative Coeff.
as x→−∞, f(x)→∞ ; as x→∞, f(x)→−∞
both ends up
as x→−∞, f(x)→−∞ ; as x→∞, f(x)→−∞
Odd degree, Positive coeff.
Odd degree, Negative coeff.
as x→−∞, f(x)→∞ ; as x→∞, f(x)→−∞
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…
11 terms
Algebra polynomials
0
1
2
3
constant degree
Linear degree
Quadratic degree
Cubic degree
0
constant degree
1
Linear degree
9 terms
algebra polynomials
degree 0
degree 1
degree 2
degree 3
constant
linear
quadratic
cubic
degree 0
constant
degree 1
linear
11 terms
Algebra Polynomials
Constant
Linear
Quadratic
Cubic
Degree of 0
Degree of 1
Degree of 2
Degree of 3
Constant
Degree of 0
Linear
Degree of 1
9 terms
Algebra- polynomials
i0
i1
i2
i3
1
i
-1
-i
i0
1
i1
i
11 terms
algebra polynomials
constant
linear
quadratic
cubic
0 degrees
1 degree
2 degrees
3 degrees
constant
0 degrees
linear
1 degree
Polynomials & Polynomial functions
monomial
the degree of a monomial
polynomial
degree of a polynomial
a real number, variable, or product of a real number and one…
exponent of a variable
monomial or a sum of monomials
greatest degree among its monomial terms
monomial
a real number, variable, or product of a real number and one…
the degree of a monomial
exponent of a variable
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