How do you factor the quadratic equation $$5x^2 - 2x - 3 = 0$$ ?

To factor $$5x^2 - 2x - 3$$ , look for two numbers that multiply to $$5 * -3 = -15$$ and add to $$-2$$ . The factors are $$3$$ and $$-5$$ . Thus, it can be factored as $$(5x + 3)(x - 1) = 0$$ .

What are the solutions to the equation $$5x^2 - 2x - 3 = 0$$ ?

The solutions are $$x = -\frac{3}{5}$$ and $$x = 1$$ .

How do you factor the quadratic equation $$x^2 - 5x - 6 = 0$$ ?

To factor $$x^2 - 5x - 6$$ , find two numbers that multiply to $$-6$$ and add to $$-5$$ . The factors are $$-6$$ and $$1$$ . Thus, it can be factored as $$(x - 6)(x + 1) = 0$$ .

What are the solutions to the equation $$x^2 - 5x - 6 = 0$$ ?

The solutions are $$x = 6$$ and $$x = -1$$ .

How do you solve the equation $$x^2 + 9 = 10x$$ by factoring?

Rearranging gives $$x^2 - 10x + 9 = 0$$ . To factor, find two numbers that multiply to $$9$$ and add to $$-10$$ . The factors are $$-1$$ and $$-9$$ . Thus, it can be factored as $$(x - 1)(x - 9) = 0$$ .

What are the solutions to the equation $$x^2 + 9 = 10x$$ ?

The solutions are $$x = 1$$ and $$x = 9$$ .

How do you factor the quadratic equation $$6x^2 - 16x + 8 = 0$$ ?

To factor $$6x^2 - 16x + 8$$ , first factor out the common term $$2$$ , giving $$2(3x^2 - 8x + 4) = 0$$ . Then, find two numbers that multiply to $$3 * 4 = 12$$ and add to $$-8$$ . The factors are $$-6$$ and $$-2$$ . Thus, it can be factored as $$2(3x - 2)(x - 2) = 0$$ .

What are the solutions to the equation $$6x^2 - 16x + 8 = 0$$ ?

The solutions are $$x = \frac{2}{3}$$ and $$x = 2$$ .

How do you factor the equation $$x^2 - 121 = 0$$ ?

This is a difference of squares, which factors as $$(x - 11)(x + 11) = 0$$ .

What are the solutions to the equation $$x^2 - 121 = 0$$ ?

The solutions are $$x = 11$$ and $$x = -11$$ .

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the importance of the discriminant in quadratic equations?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation. If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; and if $$D

What is a common mistake when solving quadratic equations by factoring?

A common mistake is failing to check if the factors are correct or overlooking the possibility of complex roots when the discriminant is negative.

Solve Quadratic Equations by Factoring Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to solve a quadratic equation by factoring?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the zero-product property?

Back

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CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

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Back

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CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

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Back

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CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

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Back

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CCSS.HSA-REI.B.4B

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