How do you factor the polynomial $$a^2 + 15a + 44$$ ?

To factor $$a^2 + 15a + 44$$ , look for two numbers that multiply to 44 and add to 15. The factors are 11 and 4, so it can be factored as $$(a + 11)(a + 4)$$ .

What is the result of dividing $$a^2 + 15a + 44$$ by $$a + 4$$ ?

Using synthetic division or polynomial long division, the result is $$a + 11$$ with a remainder of 0.

What is long division of polynomials?

Long division of polynomials is a method similar to long division with numbers, where you divide the leading term of the dividend by the leading term of the divisor, multiply, and subtract.

What is a zero of a polynomial?

A zero of a polynomial is a value of $$x$$ for which the polynomial evaluates to zero. For example, if $$f(x) = x^2 - 4$$ , then the zeros are $$x = 2$$ and $$x = -2$$ .

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.

What is the difference between a monomial, binomial, and trinomial?

A monomial has one term (e.g., $$3x$$ ), a binomial has two terms (e.g., $$x + 2$$ ), and a trinomial has three terms (e.g., $$x^2 + 3x + 4$$ ).

How do you check if a polynomial is divisible by another polynomial?

To check if a polynomial $$f(x)$$ is divisible by another polynomial $$g(x)$$ , perform polynomial long division. If the remainder is zero, then $$f(x)$$ is divisible by $$g(x)$$ .

What is the purpose of factoring polynomials?

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in finding the roots or zeros of the polynomial.

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

The roots of a polynomial are the values of $$x$$ that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial in the form $$(x - r)$$ , where $$r$$ is a root.

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA.APR.D.6, HSA.APR.B.2, HSF-IF.C.7C

Standards-aligned

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is a polynomial?

Back

FLASHCARD QUESTION

Front

What does it mean to divide polynomials?

Back

Dividing polynomials involves finding how many times one polynomial (the divisor) can fit into another polynomial (the dividend), resulting in a quotient and possibly a remainder.

Tags

CCSS.HSA.APR.D.6

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

Tags

CCSS.HSA.APR.B.2

FLASHCARD QUESTION

Front

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

15 questions

7517 01 Programming Basics

Flashcard

•

10th Grade - University

11 questions

Review A2

Flashcard

•

10th Grade

11 questions

3D Design Vocabulary Flashcard

Flashcard

•

10th Grade

12 questions

Organic 2 Exam 4 Review

Flashcard

•

10 questions

Flashcards memory game

Flashcard

•

KG - University

10 questions

Teks Rekon (Fakta, Asumsi, Opini) Flashcard

Flashcard

•

9th Grade - University

11 questions

7517 05 Structured Programming

Flashcard

•

10th Grade - University

12 questions

Descriptive adjectives for Home and Furniture

Flashcard

•

10th Grade - University

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

15 questions

Hargrett House Quiz: Community & Service

Quiz

•

5th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

10 questions

Exploring Basic Probability Concepts

Interactive video

•

6th - 10th Grade

11 questions

Adding and Subtracting Polynomials

Quiz

•

9th Grade

20 questions

Rational and Irrational Numbers, Perfect Squares, & Perfect Cube

Quiz

•

9th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

10 questions

Factoring Quadratic Expressions

Quiz

•

9th Grade

16 questions

Identifying Angles

Quiz

•

7th - 12th Grade

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade