The degree of a polynomial is...

The highest power to which the variable is raised in the polynomial.

When factoring the GCF from a polynomial, you are essentially:

Reversing the distributive property

The numerical or constant factor of a term.

What is the first step in factoring any polynomial?

Identifying the Greatest Common Factor (GCF) of the terms

An expression of a single term without addition or subtraction operations.

Associative Property of Multiplication

a\times(b\times c)=(a\times b)\times c

The leading coefficient of a polynomial is...

The coefficient of the term with the highest degree.

studbud

Algebra: Basic concepts (2)

25 termsStudBud Administration222 plays

Embark on a thrilling mathematical adventure! Dive into the world of numbers, equations, and algebraic concepts that will sharpen your problem-solving skills and empower you with the tools to tackle complex challenges. 🧮Discover the beauty of algebra as you learn about fundamental concepts like variables, equations, expressions, and more! 🌟

Flashcards25 cardsFPractice quizPHost liveL

Questions 25

Answers

1
If an algebraic expression has no common factors among its terms besides 1, it is:
Prime
Composite
A trinomial
A binomial
2
Which of the following is NOT a polynomial?
x^4-2x^3+x^2
3x^5-4x^4+6
2x^3+3x^2-5x+6
\sqrt{x+3}
3
Which expression is a binomial?
x^4
x^3-x^2+x
^{x^3+2x^2+y+1}
x^2+4x
4
Factor out14x^2-7x . What remains inside the parentheses?
2x
2x+1
2
2x-1
5
The degree of a polynomial is...
The highest power to which the variable is raised in the polynomial.
The constant term of a polynomial.
The sum of the coefficients.
The total number of terms in the polynomial.
6
Which of the following is a trinomial?
2x^2-5x+3
x^2+3x
x^3+2x^2
4x
7
Associative Property of Addition
a+(b+c)=(a+b)+c
a(b+c)=ab+ac
a+b=b+a
a\times(b\times c)=(a\times b)\times c
8
What is the GCF of12a^3 and9a^2?
3a^2
3a
12a
3
9
When factoring the GCF from a polynomial, you are essentially:
Reversing the distributive property
Distributing the terms
Dividing the terms
Multiplying the terms
10
Which expression is a quadratic?
x^3+4x^2+4x+4
x^3-x+1
x+5
3x^3+5x^2-4
11
Commutative Property of Addition
a+b=b+a
a+b=b+c
a(b+c)=ab+ac
a\times b=a+b
12
A coefficient is...
The term without a variable.
The numerical or constant factor of a term.
The highest power to which a variable is raised.
The product of two binomials.
13
What is the first step in factoring any polynomial?
Identifying the terms with coefficients
Finding the highest power of x
Dividing each term by x
Identifying the Greatest Common Factor (GCF) of the terms
14
Which of the following terms can be factored out of10x^2+5xy?
x
5x
2y
5xy
15
Which expression shows 6x^2y+9xy^2factored completely?
3xy(2x+3y)
3xy(2xy+3y)
3y(2x^2+3x)
6x(xy+y^{2)}
16
Which of the following is a monomial?
x^3+x^2
x+1
x^2
x^3-x^2+x
17
The constant term in a polynomial is...
The coefficient of the leading term.
The term with the highest power of the variable.
The term without a variable.
The term with the lowest power of the variable.
18
Factor completely 18y^3+9y^2
3y
9y^2\left(2y+1\right)
9y\left(2y^3+1\right)
9y^3\left(2+1\right)
19
Distributive Property of Addition over Multiplication
a(b-c)=ab-ac
a(b+c)=ab+ac
a+b=b+a
a\times b=b\times a
20
A monomial is...
An algebraic expression that represents a quadratic function.
An expression of a single term without addition or subtraction operations.
An algebraic expression with three terms.
A mathematical expression with two unlike terms.
21
Commutative Property of Multiplication
a+b=b+a
a\times b=b+a
a\times b=b\times a
a(b-c)=ab-ac
22
Associative Property of Multiplication
a\times b=b\times a
a\times(b\times c)=(a\times b)\times c
a(b+c)=ab+ac
a+(b+c)=(a+b)+c
23
Which expression is a common factor of9x^3 and 6x^2?
3x^2
9x
x
3
24
The leading coefficient of a polynomial is...
The constant term.
The term with the highest power of the variable.
The coefficient of the term with the highest degree.
The coefficient of the term with the lowest degree.
25
When factoring out from 4x^2+8x, what do you factor out?
4
4x
2
x

Algebra: Basic concepts (2) Flashcards | StudBud

Algebra: Basic concepts (2)

25 termsStudBud Administration222 plays

Flashcards25 cardsFPractice quizPHost liveL

Questions 25

Answers

1
If an algebraic expression has no common factors among its terms besides 1, it is:
Prime
Composite
A trinomial
A binomial
2
Which of the following is NOT a polynomial?
x^4-2x^3+x^2
3x^5-4x^4+6
2x^3+3x^2-5x+6
\sqrt{x+3}
3
Which expression is a binomial?
x^4
x^3-x^2+x
^{x^3+2x^2+y+1}
x^2+4x
4
Factor out14x^2-7x . What remains inside the parentheses?
2x
2x+1
2
2x-1
5
The degree of a polynomial is...
The highest power to which the variable is raised in the polynomial.
The constant term of a polynomial.
The sum of the coefficients.
The total number of terms in the polynomial.
6
Which of the following is a trinomial?
2x^2-5x+3
x^2+3x
x^3+2x^2
4x
7
Associative Property of Addition
a+(b+c)=(a+b)+c
a(b+c)=ab+ac
a+b=b+a
a\times(b\times c)=(a\times b)\times c
8
What is the GCF of12a^3 and9a^2?
3a^2
3a
12a
3
9
When factoring the GCF from a polynomial, you are essentially:
Reversing the distributive property
Distributing the terms
Dividing the terms
Multiplying the terms
10
Which expression is a quadratic?
x^3+4x^2+4x+4
x^3-x+1
x+5
3x^3+5x^2-4
11
Commutative Property of Addition
a+b=b+a
a+b=b+c
a(b+c)=ab+ac
a\times b=a+b
12
A coefficient is...
The term without a variable.
The numerical or constant factor of a term.
The highest power to which a variable is raised.
The product of two binomials.
13
What is the first step in factoring any polynomial?
Identifying the terms with coefficients
Finding the highest power of x
Dividing each term by x
Identifying the Greatest Common Factor (GCF) of the terms
14
Which of the following terms can be factored out of10x^2+5xy?
x
5x
2y
5xy
15
Which expression shows 6x^2y+9xy^2factored completely?
3xy(2x+3y)
3xy(2xy+3y)
3y(2x^2+3x)
6x(xy+y^{2)}
16
Which of the following is a monomial?
x^3+x^2
x+1
x^2
x^3-x^2+x
17
The constant term in a polynomial is...
The coefficient of the leading term.
The term with the highest power of the variable.
The term without a variable.
The term with the lowest power of the variable.
18
Factor completely 18y^3+9y^2
3y
9y^2\left(2y+1\right)
9y\left(2y^3+1\right)
9y^3\left(2+1\right)
19
Distributive Property of Addition over Multiplication
a(b-c)=ab-ac
a(b+c)=ab+ac
a+b=b+a
a\times b=b\times a
20
A monomial is...
An algebraic expression that represents a quadratic function.
An expression of a single term without addition or subtraction operations.
An algebraic expression with three terms.
A mathematical expression with two unlike terms.
21
Commutative Property of Multiplication
a+b=b+a
a\times b=b+a
a\times b=b\times a
a(b-c)=ab-ac
22
Associative Property of Multiplication
a\times b=b\times a
a\times(b\times c)=(a\times b)\times c
a(b+c)=ab+ac
a+(b+c)=(a+b)+c
23
Which expression is a common factor of9x^3 and 6x^2?
3x^2
9x
x
3
24
The leading coefficient of a polynomial is...
The constant term.
The term with the highest power of the variable.
The coefficient of the term with the highest degree.
The coefficient of the term with the lowest degree.
25
When factoring out from 4x^2+8x, what do you factor out?
4
4x
2
x