What is the first step in solving the equation $$x^2 + 6x - 13 = 3$$ by factoring?

The first step is to make it equal to 0 by subtracting 3 from both sides: $$x^2 + 6x - 16 = 0$$ .

How do you factor the expression $$x^2 + 12x + 35$$ ?

Look for two numbers that multiply to 35 and add to 12. The factors are 5 and 7, so it factors to $$(x + 5)(x + 7) = 0$$ .

What are the roots of the equation $$n^2 + 7n + 15 = 5$$ after rearranging?

After rearranging to $$n^2 + 7n + 10 = 0$$ , the roots are $$n = -5 and n = -2$$ .

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 zero-product property?

The zero-product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ .

How do you check if your factored solution is correct?

You can check by substituting the roots back into the original equation to see if they satisfy it.

A binomial is a polynomial with two terms, such as $$x + 5$$ or $$x - 3$$ .

What is the significance of the discriminant in a quadratic equation?

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

What is the factored form of $$x^2 - 16$$ ?

The factored form is $$(x - 4)(x + 4)$$ , which is a difference of squares.

Solving Quadratics by Factoring (a=1 or GCF) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of 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

How do you find the roots of a quadratic equation by factoring?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

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CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the GCF (Greatest Common Factor) in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. It can be factored out before applying other factoring methods.

7.

FLASHCARD QUESTION

Front

Back

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