What is the first step in solving the equation $$x^2 + 12x = 64$$ by factoring?

Rearrange the equation to set it to zero: $$x^2 + 12x - 64 = 0$$ .

How do you factor the expression $$5x^2 - 10x = 0$$ using GCF?

Factor out the GCF, which is 5x: $$5x(x - 2) = 0$$ .

What are the roots of the equation $$2x^2 - 5x + 2 = 0$$ using the SMAG method?

The roots are $$x = \frac{1}{2}$$ and $$x = 2$$ .

How do you solve the equation $$4x^2 - 9 = 0$$ using the DOS method?

Factor as $$(2x - 3)(2x + 3) = 0$$ and solve for x.

What are the solutions to the equation $$4x^2 - 9 = 0$$ ?

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

What is the significance of the discriminant in the Quadratic Formula?

The discriminant, $$b^2 - 4ac$$ , determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

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

Set the equation to zero by moving all terms to one side.

What does it mean for a quadratic equation to be factorable?

A quadratic equation is factorable if it can be expressed as a product of two binomials.

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

You can check by expanding the factored form to see if it equals the original quadratic equation.

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

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a, where the quadratic is in the form $$ax^2 + bx + c = 0$$ .

What is the importance of solving quadratics in real-world applications?

Solving quadratics can help model and solve problems in physics, engineering, finance, and many other fields.

Day 42 Solve by Factoring (1-6) and Quadratic Formula (7-11) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in the expression.

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the purpose of using the SMAG method in factoring?

Back

SMAG stands for 'Sum, Middle, and Product' and is used to factor quadratic equations by finding two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle coefficient.

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What does DOS stand for in factoring?

Back

Tags

CCSS.HSA.APR.C.4

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