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

The expression can be factored as $$(x - 4)(x + 3)$$ .

What are the roots of the equation $$x^2 - x - 12 = 0$$ ?

The roots are $$x = 4$$ and $$x = -3$$ .

What is the first step in factoring the expression $$3x^2 - 6x$$ ?

The first step is to factor out the greatest common factor (GCF), which is $$3x$$ , resulting in $$3x(x - 2) = 0$$ .

What are the solutions to the equation $$3x^2 - 6x = 0$$ ?

The solutions are $$x = 0$$ and $$x = 2$$ .

How do you factor the expression $$x^2 - 4x - 21$$ ?

The expression can be factored as $$(x - 7)(x + 3)$$ .

What are the roots of the equation $$x^2 - 4x - 21 = 0$$ ?

The roots are $$x = 7$$ and $$x = -3$$ .

How do you factor the expression $$x^2 - 9$$ ?

The expression can be factored as $$(x - 3)(x + 3)$$ .

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

The solutions are $$x = 3$$ and $$x = -3$$ .

How do you factor the expression $$x^2 + 7x + 10$$ ?

The expression can be factored as $$(x + 5)(x + 2)$$ .

What are the roots of the equation $$x^2 + 7x + 10 = 0$$ ?

The roots are $$x = -5$$ and $$x = -2$$ .

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, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Factoring Quadratic Equations Flashcard Flashcards

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1.

FLASHCARD QUESTION

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

2.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

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

Back

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