Factor the sum of cubes: $$125x^3 - 8$$

$$\text{(5x - 2)(25x^2 + 10x + 4)}$$

What is the formula for factoring the sum of cubes?

The formula is: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$ .

What is the formula for factoring the difference of cubes?

The formula is: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ .

How do you factor a quadratic expression of the form $$ax^2 + bx + c$$ ?

Look for two numbers that multiply to $$ac$$ and add to $$b$$ .

What is the first step in factoring a quadratic expression?

Identify the coefficients a, b, and c in the expression $$ax^2 + bx + c$$ .

What is a common method for factoring quadratics when a = 1?

Look for two numbers that add to b and multiply to c.

What is the significance of the discriminant in quadratic equations?

The discriminant $$D = b^2 - 4ac$$ determines the nature of the roots.

What does it mean if the discriminant is positive?

If $$D > 0$$ , the quadratic has two distinct real roots.

What does it mean if the discriminant is zero?

If $$D = 0$$ , the quadratic has exactly one real root (a repeated root).

Factoring Quadratics and Sum/Difference of Cubes Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

(x - 9)(x - 5)

2.

FLASHCARD QUESTION

Front

Back

(x + 5)(x + 8)

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

(x + 1)(x - 1)

5.

FLASHCARD QUESTION

Front

Back

(x + 5)(x - 5)

6.

FLASHCARD QUESTION

Front

Define the difference of squares.

Back

7.

FLASHCARD QUESTION

Front

What is the formula for factoring a perfect square trinomial?

Back

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