How do you factor the expression $$b^2 + 8b - 33$$ ?

To factor $$b^2 + 8b - 33$$ , find two numbers that multiply to -33 and add to 8. The factors are (b + 11)(b - 3).

What are the roots of the equation $$n^2 + 3n = 0$$ ?

The roots are found by factoring: $$n(n + 3) = 0$$ , giving roots n = 0 and n = -3.

How do you solve $$9x^2 - 12x + 4 = 0$$ by factoring?

This can be factored as $$(3x - 2)^2 = 0$$ , leading to the double root $$x = \frac{2}{3}$$ .

What is the significance of the roots of a quadratic equation?

The roots represent the x-values where the quadratic function intersects the x-axis.

How do you factor the expression $$m^2 + 15m + 72 - 18$$ ?

First, simplify to $$m^2 + 15m + 54 = 0$$ , then factor to get (m + 9)(m + 6) = 0, giving roots m = -9 and m = -6.

What is the factored form of $$n^2 - 10n + 24 = 0$$ ?

The factored form is (n - 4)(n - 6) = 0, with roots n = 4 and n = 6.

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

The first step is to set the equation to zero, if it is not already in that form.

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

It means the discriminant is less than zero, indicating that the roots are complex or imaginary.

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

You can check by expanding the factors back into the original quadratic equation.

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

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a, according to Vieta's formulas.

What is the importance of factoring in solving quadratic equations?

Factoring simplifies the process of finding the roots, making it easier to solve the equation.

Solve by Factoring Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the process of solving a quadratic equation by factoring?

Back

The process involves expressing the quadratic equation in the form of a product of two binomials, setting each factor equal to zero, and solving for the variable.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does it mean for a quadratic equation to have real solutions?

Back

A quadratic equation has real solutions if the discriminant (b^2 - 4ac) is greater than or equal to zero.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

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

Back

Tags

CCSS.HSA-REI.B.4B

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