How do you factor the expression $$5x^3 - 7x^2$$ ?

To factor $$5x^3 - 7x^2$$ , you can take out the common factor, which is $$x^2$$ . The factored form is $$x^2(5x - 7)$$ .

What is the process to solve the equation $$2x^2 - 8x = 0$$ ?

To solve $$2x^2 - 8x = 0$$ , factor out the common term: $$2x(x - 4) = 0$$ . Then, set each factor to zero: $$2x = 0$$ (gives $$x = 0$$ ) and $$x - 4 = 0$$ (gives $$x = 4$$ ). Thus, the solutions are $$x = 0$$ or $$x = 4$$ .

What is the product of the expressions $$(x + 3)(x^2 - x + 4)$$ ?

The product of $$(x + 3)(x^2 - x + 4)$$ is $$x^3 + 2x^2 + x + 12$$ .

What is the degree of a polynomial?

The degree of a polynomial is the highest power of the variable in the expression. For example, in $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

How do you apply the Zero-Product Property to solve $$ (x - 11)(5x + 1) = 0 $$ ?

Set each factor to zero: $$x - 11 = 0$$ (gives $$x = 11$$ ) and $$5x + 1 = 0$$ (gives $$x = -\frac{1}{5}$$ ). Thus, the solutions are $$x = 11$$ or $$x = -\frac{1}{5}$$ .

What is the difference between a monomial and a polynomial?

A monomial is an algebraic expression with only one term, while a polynomial can have multiple terms. For example, $$3x$$ is a monomial, and $$3x + 2x^2 - 5$$ is a polynomial.

What is a factor of a polynomial?

A factor of a polynomial is an expression that divides the polynomial evenly, resulting in another polynomial. For example, $$(x - 2)$$ is a factor of $$x^2 - 2x + 4$$ .

What is the significance of the leading coefficient in a polynomial?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial's graph.

How do you determine if a polynomial is prime?

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials. For example, $$x^2 + 1$$ is prime.

What is the standard form of a polynomial?

The standard form of a polynomial is written in descending order of the degree of its terms. For example, $$4x^3 + 2x^2 - x + 7$$ is in standard form.

What is the relationship between the roots of a polynomial and its factors?

The roots of a polynomial are the values of the variable that make the polynomial equal to zero. Each root corresponds to a factor of the polynomial.

Resource Library

Math

Algebra

Expressions And Equations

Algebraic Expressions And Equations

Algebraic Expressions and Equations

Flashcard

•

Mathematics

•

11th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, 6.EE.A.2B, HSA.APR.A.1

Standards-aligned

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is an algebraic expression?

Back

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It does not have an equality sign.

Tags

CCSS.6.EE.A.2B

FLASHCARD QUESTION

Front

What is the Zero-Product Property?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

FLASHCARD QUESTION

Front

What does it mean to factor an expression?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

What is a polynomial?

Back

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

12 questions

Hazard Profiles and Tectonic Hazards Flashcard

Flashcard

•

11th Grade - University

13 questions

Types and Components of Computer Systems

Flashcard

•

9th - 12th Grade

13 questions

Money

Flashcard

•

9th - 12th Grade

10 questions

Synonyms

Flashcard

•

11th Grade

15 questions

cars

Flashcard

•

KG - University

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

10 questions

Probability Practice

Quiz

•

4th Grade

15 questions

Probability on Number LIne

Quiz

•

4th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

6 questions

Appropriate Chromebook Usage

Lesson

•

7th Grade

10 questions

Greek Bases tele and phon

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

23 questions

TSI Math Vocabulary

Quiz

•

10th - 12th Grade

80 questions

ACT Math Important Vocabulary

Quiz

•

11th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

11 questions

Slopes of Parallel and Perpendicular Lines

Quiz

•

7th - 11th Grade

13 questions

Identify Transformations in Geometry

Quiz

•

8th - 12th Grade

20 questions

Quadratic Transformations Review

Quiz

•

9th - 12th Grade

10 questions

Area of 2D Shapes

Quiz

•

7th - 11th Grade