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

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15 questions

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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.

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