What are the steps to factor the quadratic $$x^2 + 13x + 12$$ ?

1. Identify two numbers that multiply to $$12$$ (the constant term) and add to $$13$$ (the coefficient of $$x$$ ). 2. The numbers are $$12$$ and $$1$$ . 3. Factor as $$(x + 12)(x + 1) = 0$$ .

What are the roots of the equation $$p^2 - 4p - 32 = 0$$ ?

The roots are found by factoring: $$(p - 8)(p + 4) = 0$$ , giving solutions $$p = 8$$ and $$p = -4$$ .

How do you determine the solutions from the factored form of a quadratic equation?

Set each factor equal to zero and solve for the variable. For example, from $$(x + 4)(x - 3) = 0$$ , set $$x + 4 = 0$$ and $$x - 3 = 0$$ .

What is the relationship between the coefficients and the 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 $$c/a$$ .

How do you solve the equation $$5v^2 - 21v + 18 = 0$$ by factoring?

Factor to get $$(5v - 3)(v - 6) = 0$$ , leading to solutions $$v = \frac{3}{5}$$ and $$v = 6$$ .

What is the first step in solving a quadratic equation by factoring?

The first step is to ensure the equation is set to zero, typically in the form $$ax^2 + bx + c = 0$$ .

What does it mean if a quadratic equation has no real solutions?

If a quadratic equation has no real solutions, it means the parabola does not intersect the x-axis, which occurs when the discriminant $$b^2 - 4ac

What is the discriminant of a quadratic equation?

The discriminant is the expression $$b^2 - 4ac$$ that determines the nature of the roots of the quadratic equation.

How can you check if your factored form of a quadratic is correct?

You can check by expanding the factored form back into standard form and ensuring it matches the original quadratic equation.

What is the importance of the leading coefficient in a quadratic equation?

The leading coefficient affects the direction of the parabola (upward if positive, downward if negative) and the width of the parabola.

Solving Quadratics by Factoring Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to factor a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the Zero-Product Property?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

How do you solve a quadratic equation by factoring?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the significance of the constant term in a quadratic equation?

Back

The constant term affects the vertical position of the parabola represented by the quadratic equation and is the product of the roots when factored.

Tags

CCSS.HSF-IF.C.7A

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