Factoring

Front

What is the factored form of the quadratic expression x² - 19x - 42?

Back

(x - 21)(x + 2)

Front

If a trinomial ax² + bx + c has a negative 'c' value, what can be inferred about the signs of its binomial factors?

Back

The signs are one + and one -.

Front

How do you factor the trinomial 3x² + 5x - 12 completely?

Back

(3x - 4)(x + 3)

Front

What is an example of a difference of perfect squares?

Back

9x² - 100

Front

What is the completely factored form of 4x³ + 32x² - 80x?

Back

4x(x + 10)(x - 2)

Front

What is the general form of a quadratic equation?

Back

ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the leading coefficient 'a' in a quadratic equation?

Back

It determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression and factor by grouping.

Front

What is the difference of squares formula?

Back

a² - b² = (a - b)(a + b) for any real numbers a and b.

Front

How can you identify a perfect square trinomial?

Back

It can be expressed as (a ± b)², where a² and b² are the first and last terms.