What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

How do you solve a quadratic equation by factoring?

To solve by factoring, express the quadratic in the form $$(x - p)(x - q) = 0$$ , then set each factor to zero: $$x - p = 0$$ and $$x - q = 0$$ .

What is a polynomial function?

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

What does it mean for a polynomial to be factored completely?

A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system (e.g., real or complex numbers).

What is the role 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 graph.

How do you identify the zeros of a polynomial function?

To identify the zeros, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

What is the Fundamental Theorem of Algebra?

The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

What is the process of long division for polynomials?

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by that result, and subtracting from the dividend, repeating until the remainder is of lower degree.

Factoring and Finding Polynomial Zeros Flashcard

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What are polynomial zeros?

Back

Polynomial zeros are the values of x that make the polynomial equal to zero. They are also known as roots or solutions of the polynomial.

Tags

CCSS.HSF-IF.C.7C

3.

FLASHCARD QUESTION

Front

How do you find rational zeros of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

5.

FLASHCARD QUESTION

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.

6.

FLASHCARD QUESTION

Front

How do you factor a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring techniques such as difference of squares or the quadratic formula.

7.

FLASHCARD QUESTION

Front

What is the difference of squares?

Back

Tags

CCSS.HSA.APR.C.4

Create a free account and access millions of resources

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

By signing up, you agree to our Terms of Service & Privacy Policy

Already have an account?

Similar Resources on Wayground

12 questions

Untitled Flashcards

Flashcard

•

University

12 questions

Present perfect Vs past tense

Flashcard

•

University

10 questions

Mathematics Glossary

Flashcard

•

KG

10 questions

TARJETAS DIDÁCTICAS DOCTRINA POLICIAL

Flashcard

•

12th Grade

10 questions

Disney descendants flashcard

Flashcard

•

KG

10 questions

Relación e Importancia de la Epistemología con la Educación

Flashcard

•

University

10 questions

SUP E3 - PART 1

Flashcard

•

University

Popular Resources on Wayground

10 questions

Honoring the Significance of Veterans Day

Interactive video

•

6th - 10th Grade

10 questions

Exploring Veterans Day: Facts and Celebrations for Kids

Interactive video

•

6th - 10th Grade

19 questions

Veterans Day

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

15 questions

Circuits, Light Energy, and Forces

Quiz

•

5th Grade

6 questions

FOREST Self-Discipline

Lesson

•

1st - 5th Grade

7 questions

Veteran's Day

Interactive video

•

3rd Grade

20 questions

Weekly Prefix check #2

Quiz

•

4th - 7th Grade

Discover more resources for Mathematics

19 questions

Explore Triangle Congruence and Proofs

Quiz

•

9th - 12th Grade

15 questions

Identify Triangle Congruence Criteria

Quiz

•

9th - 12th Grade

23 questions

Similar Figures

Quiz

•

9th - 12th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

10 questions

Arithmetic Sequences

Quiz

•

9th - 12th Grade

20 questions

Week 4 Memory Builder 1 (Squares and Roots) Term 2

Quiz

•

9th - 12th Grade

12 questions

Simplifying Roots

Quiz

•

9th - 12th Grade

12 questions

Identifying Ratios

Quiz

•

6th - 12th Grade