How do you factor a quadratic equation of the form $$ax^2 + bx + c = 0$$ ?

To factor a quadratic equation, find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the equation as a product of two binomials.

How do you solve the equation $$5x^2 + 15x = 0$$ by factoring?

Factor out the GCF: $$5x(x + 3) = 0$$ . Then set each factor to zero: $$5x = 0$$ or $$x + 3 = 0$$ , giving solutions $$x = 0$$ and $$x = -3$$ .

What are the steps to factor the expression $$x^2 - 9x + 20$$ ?

1. Identify two numbers that multiply to 20 and add to -9. 2. The numbers are -4 and -5. 3. Rewrite as $$(x - 4)(x - 5) = 0$$ .

A binomial is a polynomial with exactly two terms, such as $$x + 2$$ or $$3x^2 - 5$$ .

How do you find the roots of the equation $$(x - 5)(x + 2) = 0$$ ?

Set each factor to zero: $$x - 5 = 0$$ gives $$x = 5$$ , and $$x + 2 = 0$$ gives $$x = -2$$ .

What is the relationship between the coefficients and roots of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-b/a$$ and the product of the roots is $$c/a$$ .

What is the purpose of factoring in solving equations?

Factoring simplifies the equation, making it easier to find the roots or solutions.

A trinomial is a polynomial with three terms, such as $$x^2 + 5x + 6$$ .

How do you check if your factored solution is correct?

Multiply the factors back together to see if you obtain the original expression.

What is the difference between factoring by grouping and factoring by the GCF?

Factoring by grouping involves rearranging terms and factoring pairs, while factoring by the GCF involves finding the largest common factor of all terms.

What is a polynomial?

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients, such as $$2x^3 - 4x + 7$$ .

Solve by Factoring Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

2.

FLASHCARD QUESTION

Front

What is the Zero Product Property?

Back

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

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

13 questions

Types and Components of Computer Systems

Flashcard

•

9th - 12th Grade

13 questions

Money

Flashcard

•

9th - 12th Grade

10 questions

Essential Housework Tasks

Flashcard

•

10th Grade

9 questions

Trigonometric Ratios - Recap For Math Q4 W1

Flashcard

•

9th Grade

11 questions

Monomios e Polinomios

Flashcard

•

8th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

20 questions

Figurative Language Review

Quiz

•

6th Grade

Discover more resources for Mathematics

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

13 questions

Model Exponential Growth and Decay Scenarios

Quiz

•

9th - 12th Grade

27 questions

7.2.3 Quadrilateral Properties

Quiz

•

9th - 12th Grade

16 questions

Converting Improper Fractions to Mixed Numbers

Quiz

•

4th - 10th Grade

10 questions

Simplifying Expressions by Combining Like Terms

Interactive video

•

6th - 10th Grade

10 questions

Simplifying Expressions with the Distributive Property

Interactive video

•

6th - 10th Grade

10 questions

Key Features of Quadratic Functions

Interactive video

•

8th - 12th Grade